{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.linalg import eigh_tridiagonal\n", "from scipy.integrate import quad\n", "import sympy as sym\n", "sym.init_printing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\begin{bmatrix}\\frac{1}{\\Delta y^2}+mL^2V_1 & -\\frac{1}{2 \\Delta y^2} & 0 & 0...\\\\ -\\frac{1}{2 \\Delta y^2} & \\frac{1}{\\Delta y^2}+mL^2V_2 & -\\frac{1}{2 \\Delta y^2} & 0... \\\\ ...& ... & ... & -\\frac{1}{2 \\Delta y^2}\\\\...0 & 0 & -\\frac{1}{2 \\Delta y^2} & \\frac{1}{\\Delta y^2}+mL^2V_{N-1} \\\\ \\end{bmatrix} \\begin{bmatrix} \\psi_1 \\\\ \\psi_2 \\\\ ... \\\\ \\psi_{N-1} \\end{bmatrix} = mL^2 E \\begin{bmatrix} \\psi_1 \\\\ \\psi_2 \\\\ ... \\\\ \\psi_{N-1} \\end{bmatrix} $$\n", "\n", "$$ \\psi_0 = \\psi_N = 0$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define what $N$ and $dy$ is" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "N = 100\n", "dy = 1/N\n", "y = np.linspace(0, 1, N+1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define potential $mL^2 V$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "#np.where(((y<0.25) | (y>0.75)), 1e8, 0)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def mL2V(y):\n", " #return 1000*np.sin(20*y) * y**4 \n", " return np.where(((y<0.25) | (y>0.75)), 500, 0)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "d = 1/dy**2 + mL2V(y)[1:-1]\n", "e = -1/(2*dy**2) * np.ones(len(d)-1)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "w, v = eigh_tridiagonal(d, e)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,5))\n", "plt.plot(y, mL2V(y), lw=3)\n", "plt.title('Potential', fontsize=30)\n", "plt.ylabel('$V/V_0$', fontsize=25)\n", "plt.xlabel('$x/L$', fontsize=25)\n", "plt.grid()\n", "#plt.savefig('v3p1.png', dpi=200)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,5))\n", "plt.plot(y[1:-1], v.T[0], label=\"1\")\n", "plt.plot(y[1:-1], v.T[1], label=\"2\")\n", "plt.plot(y[1:-1], v.T[2], label=\"3\")\n", "plt.plot(y[1:-1], v.T[3], label=\"4\")\n", "plt.title('Eigenstates', fontsize=20)\n", "plt.ylabel('$\\psi$', fontsize=15)\n", "plt.xlabel('$x/L$', fontsize=15)\n", "plt.grid()\n", "plt.legend()\n", "plt.savefig('v3p2.png', dpi=200)\n", "\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$mL^2 E/\\\\hbar^2$')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.bar(np.arange(0, 10, 1), w[0:10])\n", "plt.ylabel('$mL^2 E/\\hbar^2$', fontsize=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solving Semi-analytically for Solutions ###\n", "\n", "We are assuming the solutions to the finite square well look like sinusoids in the well and decaying exponentials outside of it. That means we are looking for solutions of the form $ e^{-\\alpha x} $ outside the well and of the form $ sin(k x) $ or $ cos(k x) $, but not a superposition of both due to potential symmetry, within the well.\n", "\n", "By setting $ y = \\alpha L/2 $ and $ x = k L / 2 $ we arrive at two solutions which can be solved simultaenously:\n", "\n", "$ y = x tan (x) $ and $ x^2 + y^2 = R^2_0 $ where $ R^2_0 = \\frac{2 m L^2 V_0}{4 \\hbar } $" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "from sympy import Matrix, exp, sin, cos, integrate, oo, Eq, Rational, lambdify\n", "\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left( \\alpha, \\ L, \\ k, \\ E, \\ \\hbar, \\ V_{0}, \\ V, \\ m\\right)$" ], "text/plain": [ "(α, L, k, E, h̅, V₀, V, m)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "alpha, L, k, E, hbar, V0, V, m = sym.symbols(\"alpha L k E hbar V_0 V m\", real=True, positive=True)\n", "alpha, L, k, E, hbar, V0, V, m" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10,6))\n", "\n", "plt.title('Finite Square Well', fontsize=20)\n", "plt.ylim(0, 10)\n", "\n", "\n", "line_color = None\n", "piranges = [(0, np.pi/2), (np.pi/2, 3*np.pi/2), (3*np.pi/2, 5*np.pi/2), (5*np.pi/2, 7*np.pi/2), ]\n", "for xlow, xhi in piranges:\n", " x = np.linspace(xlow+0.01, xhi-.01, 200)\n", " y = x*np.tan(x)\n", " if not line_color:\n", " lines = plt.plot(x,y, label='x tan(x)')\n", " line_color = lines[-1].get_color()\n", " else:\n", " plt.plot(x,y, color=line_color)\n", "\n", "\n", "plt.ylabel('y = kL / 2', fontsize=15)\n", "plt.xlabel('$ x = \\\\alpha L/2$', fontsize=15)\n", "plt.grid()\n", "#xmin, xmax, ymin, ymax = plt.axis()\n", "\n", "# Plot the circles\n", "theta = np.linspace(0, np.pi, 100)\n", "for r in (2,4,6,8,9):\n", " xc = r * np.sin(theta)\n", " yc = r * np.cos(theta)\n", " plt.plot(xc,yc, label=\"$x^2 + y^2={}$\".format(r*r), linestyle='dotted')\n", "\n", "# Plot the asymptotes\n", "ymin, ymax = plt.gca().get_ylim()\n", "xvlines = ( [avline[1] for avline in piranges])\n", "plt.vlines(xvlines, ymin, ymax, linestyle='dashed', color='orange', lw=3)\n", "plt.legend()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It was kind of tricky to work out how many roots I would expect to find and whereabouts I would expect to find them. This is kind of important if we want to bracket the roots in a root finding algorithm." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def fn(r):\n", " n = int(r/np.pi)+1\n", " print(\"Expect to find {} roots\".format(n))\n", " for i in range(0,n):\n", " print (\"Root {} between {} and {}\".format(i+1, i*np.pi, (i+0.5)*np.pi))" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Expect to find 2 roots\n", "Root 1 between 0.0 and 1.5707963267948966\n", "Root 2 between 3.141592653589793 and 4.71238898038469\n" ] } ], "source": [ "fn(4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are looking for some piecewise solutions to Schrödinger's equation.\n", "\n", "$$ \\left [ \\frac{- \\hbar^2}{2m} \\frac{\\partial}{\\partial x^2} + V(x,t) \\right ] \\Psi (x,t) = E \\, \\Psi (x,t) $$\n", "\n", "If we multiply through by $ -\\frac{2m}{\\hbar^2} $ and do some rearranging we end up with:\n", "\n", "$$ \\frac{\\partial \\Psi (x,t) }{\\partial x^2} + \\frac{2m}{\\hbar^2} (E - V ) \\, \\Psi (x,t) = 0 $$\n", "\n", "If $ E \\gt V $ then the solutions must be a decaying exponential. If $ E \\lt V $ then the solutions will be sinusoids of various frequencies.\n", "\n", "The intersectons of the circles and the graphs determine the fixed energies where:\n", "\n", "$$ k^2 = \\frac{2mE}{\\hbar^2} \\mbox{ and } \\alpha^2 = \\frac{2m(V_0 - E)}{\\hbar^2} $$\n", "\n", "and the square of the radius is proportional the to the depth of the finite potential:\n", "\n", "$$ R^2 = k^2 + \\alpha^2 = \\left( \\frac{2 m V_0}{\\hbar^2} \\right) $$\n", "\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left( \\alpha, \\ L, \\ k, \\ E, \\ \\hbar, \\ V_{0}, \\ x, \\ A, \\ m\\right)$" ], "text/plain": [ "(α, L, k, E, h̅, V₀, x, A, m)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "alpha, L, k, E, hbar, V0, x, A, m = sym.symbols(\"alpha L k E hbar V_0 x A m\", real=True, positive=True)\n", "alpha, L, k, E, hbar, V0, x, A, m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we want to set up a joining of the two wavefunctions $ e^{-\\alpha x} $ and $ \\cos(kx) $ at the point x = L/2 to be continuous and also we want its derivatives joined be continuous also.\n", "\n", "Therefore:\n", "\n", "$$ e^{-\\alpha x} = \\cos(kx) $$\n", "\n", "and it's derivative is:\n", "\n", "$$ -\\alpha e^{-\\alpha x} = -k \\sin (kx) $$\n", "\n", "If we substitute one of the join points x = L/2 we get\n", "\n", "$$ e^{-\\frac{\\alpha L}{2}} = \\cos \\left( \\frac{k L}{2} \\right) $$\n", "\n", "If we agree to set L = 2 then this simplifies to\n", "\n", "\n", "$$ e^{- \\alpha} = \\cos \\left( k \\right) $$\n", "\n", "and\n", "\n", "$$ -\\alpha e^{-\\alpha } = -k \\sin (k) $$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}e^{- \\alpha} & - \\cos{\\left(k \\right)}\\\\- \\alpha e^{- \\alpha} & k \\sin{\\left(k \\right)}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ -α ⎤\n", "⎢ ℯ -cos(k) ⎥\n", "⎢ ⎥\n", "⎢ -α ⎥\n", "⎣-α⋅ℯ k⋅sin(k)⎦" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m1 = sym.Matrix([[exp(-alpha), -cos(k)],[-alpha*exp(-alpha), k*sin(k)]])\n", "m1" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle - \\alpha e^{- \\alpha} \\cos{\\left(k \\right)} + k e^{- \\alpha} \\sin{\\left(k \\right)}$" ], "text/plain": [ " -α -α \n", "- α⋅ℯ ⋅cos(k) + k⋅ℯ ⋅sin(k)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m1.det()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle - \\alpha \\cos{\\left(k \\right)} + k \\sin{\\left(k \\right)} = 0$" ], "text/plain": [ "-α⋅cos(k) + k⋅sin(k) = 0" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mdet = sym.simplify(m1.det()/(sym.exp(-alpha)))\n", "sym.Eq(mdet, 0)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle k \\sin{\\left(k \\right)} - k \\cos{\\left(k \\right)} \\tan{\\left(k \\right)}$" ], "text/plain": [ "k⋅sin(k) - k⋅cos(k)⋅tan(k)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mdet.subs(alpha, k*sym.tan(k))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle 0$" ], "text/plain": [ "0" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sym.simplify(_)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\alpha e^{- \\alpha} & - \\alpha \\cos{\\left(k \\right)}\\\\- \\alpha e^{- \\alpha} & k \\sin{\\left(k \\right)}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ -α ⎤\n", "⎢α⋅ℯ -α⋅cos(k)⎥\n", "⎢ ⎥\n", "⎢ -α ⎥\n", "⎣-α⋅ℯ k⋅sin(k) ⎦" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "slice = m1[0,:]*alpha\n", "m1[0,:] = slice\n", "m1" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}0 & - \\alpha \\cos{\\left(k \\right)} + k \\sin{\\left(k \\right)}\\end{matrix}\\right]$" ], "text/plain": [ "[0 -α⋅cos(k) + k⋅sin(k)]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "row = m1[1,:] + sym.Matrix(slice)\n", "row" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\alpha e^{- \\alpha} & - \\alpha \\cos{\\left(k \\right)}\\\\0 & - \\alpha \\cos{\\left(k \\right)} + k \\sin{\\left(k \\right)}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ -α ⎤\n", "⎢α⋅ℯ -α⋅cos(k) ⎥\n", "⎢ ⎥\n", "⎣ 0 -α⋅cos(k) + k⋅sin(k)⎦" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m1[1,:] = row\n", "m1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However $ \\displaystyle \\alpha \\cos{\\left(k \\right)} - k \\sin{\\left(k \\right )} = 0 $ so that value ought to be replaced by zero in the matrix also." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\alpha e^{- \\alpha} & - \\alpha \\cos{\\left(k \\right)}\\\\0 & 0\\end{matrix}\\right]$" ], "text/plain": [ "⎡ -α ⎤\n", "⎢α⋅ℯ -α⋅cos(k)⎥\n", "⎢ ⎥\n", "⎣ 0 0 ⎦" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m1[1,1]=0\n", "m1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This means $ \\begin{pmatrix}e^{-\\alpha} & -\\cos(k)\\\\ 0 & 0 \\end{pmatrix} \\begin{pmatrix}A\\\\B\\end{pmatrix} = \\begin{pmatrix}0\\\\0\\end{pmatrix} $ or that $ A e^{- \\alpha} -B \\cos(k) = 0 $\n", "\n", "Therefore we can write $ A = B \\cos(k) e^{ \\alpha} $ or $ B = A \\sec(k) e^{ -\\alpha } $ and we can set $ A = 1 $ for the pre normalised value.\n", "\n", "Now if assume by the same symmetry argument that half of the wave function probability density function integral must be 0.5 then we should be able to compute both A and B." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}e^{- \\alpha} & - \\sin{\\left(k \\right)}\\\\- \\alpha e^{- \\alpha} & - k \\cos{\\left(k \\right)}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ -α ⎤\n", "⎢ ℯ -sin(k) ⎥\n", "⎢ ⎥\n", "⎢ -α ⎥\n", "⎣-α⋅ℯ -k⋅cos(k)⎦" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m2 = sym.Matrix([[exp(-alpha), -sin(k)],[-alpha*exp(-alpha), -k*cos(k)]])\n", "m2" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle - \\alpha e^{- \\alpha} \\sin{\\left(k \\right)} - k e^{- \\alpha} \\cos{\\left(k \\right)}$" ], "text/plain": [ " -α -α \n", "- α⋅ℯ ⋅sin(k) - k⋅ℯ ⋅cos(k)" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m2.det()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle - \\alpha \\sin{\\left(k \\right)} - k \\cos{\\left(k \\right)} = 0$" ], "text/plain": [ "-α⋅sin(k) - k⋅cos(k) = 0" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mdet = sym.simplify(m2.det()/(sym.exp(-alpha)))\n", "sym.Eq(mdet, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compute the normalisation constant for cos(kx) ###" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle e^{- \\alpha x}$" ], "text/plain": [ " -α⋅x\n", "ℯ " ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f1 = exp(- alpha * x)\n", "f1" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle A \\cos{\\left(k x \\right)}$" ], "text/plain": [ "A⋅cos(k⋅x)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f2 = A * cos(k*x)\n", "f2" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle A \\sin{\\left(k x \\right)}$" ], "text/plain": [ "A⋅sin(k⋅x)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f3 = A*sin(k*x)\n", "f3" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{A^{2} \\left(\\frac{k}{2} + \\frac{\\sin{\\left(k \\right)} \\cos{\\left(k \\right)}}{2}\\right)}{k} + \\frac{e^{- 2 \\alpha}}{2 \\alpha}$" ], "text/plain": [ " 2 ⎛k sin(k)⋅cos(k)⎞ \n", "A ⋅⎜─ + ─────────────⎟ -2⋅α\n", " ⎝2 2 ⎠ ℯ \n", "────────────────────── + ─────\n", " k 2⋅α " ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nf1 = integrate(f2**2, (x, 0, 1)) + integrate(f1**2, (x, 1, oo))\n", "nf1" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{A^{2} \\left(\\frac{k}{2} - \\frac{\\sin{\\left(k \\right)} \\cos{\\left(k \\right)}}{2}\\right)}{k} + \\frac{e^{- 2 \\alpha}}{2 \\alpha}$" ], "text/plain": [ " 2 ⎛k sin(k)⋅cos(k)⎞ \n", "A ⋅⎜─ - ─────────────⎟ -2⋅α\n", " ⎝2 2 ⎠ ℯ \n", "────────────────────── + ─────\n", " k 2⋅α " ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nf2 = integrate(f3**2, (x, 0, 1)) + integrate(f1**2, (x, 1, oo))\n", "nf2" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{A^{2} \\left(\\frac{k}{2} + \\frac{\\sin{\\left(k \\right)} \\cos{\\left(k \\right)}}{2}\\right)}{k} + \\frac{e^{- 2 \\alpha}}{2 \\alpha} = \\frac{1}{2}$" ], "text/plain": [ " 2 ⎛k sin(k)⋅cos(k)⎞ \n", "A ⋅⎜─ + ─────────────⎟ -2⋅α \n", " ⎝2 2 ⎠ ℯ \n", "────────────────────── + ───── = 1/2\n", " k 2⋅α " ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e1 = Eq(nf1, Rational(1,2))\n", "e1" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{A^{2} \\left(\\frac{k}{2} - \\frac{\\sin{\\left(k \\right)} \\cos{\\left(k \\right)}}{2}\\right)}{k} + \\frac{e^{- 2 \\alpha}}{2 \\alpha} = \\frac{1}{2}$" ], "text/plain": [ " 2 ⎛k sin(k)⋅cos(k)⎞ \n", "A ⋅⎜─ - ─────────────⎟ -2⋅α \n", " ⎝2 2 ⎠ ℯ \n", "────────────────────── + ───── = 1/2\n", " k 2⋅α " ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e2 = Eq(nf2, Rational(1,2))\n", "e2" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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jg+16qN7uoJPa39sXie07lkIB864c/0sDOUs0QWnZ9HJIesb2/QTHMRGYpaV3K2wK22cTXMcekh6uOrcqsbofRGzJcIntXetVAKdITjaa8yqxR0zT/KF0/f3ELyucZvs6ogiwpzsN3kuNbSMKmveWRPZ4+eN5PUCpbJYPzCSUzWjyVaovAdvnpevGAAtTBAbgNcUWA0MIi2GepDttbw7MtL29pOeKmECSYxPCBZxBhKk3TWP/tIDuZxHKay1JL6Xxipr3MIrddvVDidKNWj5QIYQX0b0f4zuUiMTMJhLMKn8VjmUo8Jg+2GvnB0QIeUZa/YvCG0RIeTqxP/RU4JfU37A+NyQ9QESNvpI53ON5pwLLscDPeyrjhx1lUt9ygJR8NZ/4ed1h7Zant8L2F4mI06Ci6o9sHwZ8SdKIpo1LNERp2SwHSLkjlxNV5CXqQNL1ROLdJwvs9l1iU6wSPcT/AzBPQAShJOw4AAAAAElFTkSuQmCC\n", "text/latex": [ "$\\displaystyle A = \\frac{\\sqrt{2} \\sqrt{k} \\sqrt{\\frac{\\alpha e^{2 \\alpha} - 1}{2 k + \\sin{\\left(2 k \\right)}}} e^{- \\alpha}}{\\sqrt{\\alpha}}$" ], "text/plain": [ " ________________ \n", " ╱ 2⋅α \n", " ╱ α⋅ℯ - 1 -α\n", " √2⋅√k⋅ ╱ ────────────── ⋅ℯ \n", " ╲╱ 2⋅k + sin(2⋅k) \n", "A = ───────────────────────────────\n", " √α " ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Compute the normalisation value\n", "normalisation1 = sym.simplify(sym.solveset(e1, A).args[0])\n", "Eq(A, normalisation1)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle A = \\frac{\\sqrt{2} \\sqrt{k} \\sqrt{\\frac{\\alpha e^{2 \\alpha} - 1}{2 k - \\sin{\\left(2 k \\right)}}} e^{- \\alpha}}{\\sqrt{\\alpha}}$" ], "text/plain": [ " ________________ \n", " ╱ 2⋅α \n", " ╱ α⋅ℯ - 1 -α\n", " √2⋅√k⋅ ╱ ────────────── ⋅ℯ \n", " ╲╱ 2⋅k - sin(2⋅k) \n", "A = ───────────────────────────────\n", " √α " ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Compute the normalisation value\n", "normalisation2 = sym.simplify(sym.solveset(e2, A).args[0])\n", "Eq(A, normalisation2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Numerical Solution ###\n", "\n", "Now to find the solutions for $ \\alpha $ and k which we are going to have to solve for numerically." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import root_scalar" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\alpha^2 + k^2 = R_0^2 $$\n", "\n", "and since we know\n", "\n", "$$ \\alpha = k \\tan k $$\n", "\n", "then we can substitute that into our first equation to get:\n", "\n", "$$ \\left( k^2 \\tan^2(k) \\right) + k^2 = R_0^2 \\Rightarrow k^2( 1 + \\tan^2(k)) = k^2 \\sec^2(k) = R_0^2 $$" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "def rootfn(x, r0):\n", " return x**2/np.cos(x)**2-r0**2" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-1.00000000e+00 -9.68591166e-01 -8.62011436e-01 -6.34459096e-01\n", " -1.69448083e-01 8.43146052e-01 3.38649084e+00 1.17599051e+01\n", " 6.36538288e+01 6.58079015e+32]\n" ] } ], "source": [ "x1 = np.linspace(0, np.pi/2, 10)\n", "y1 = rootfn(x1, 1)\n", "print (y1)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ " converged: True\n", " flag: 'converged'\n", " function_calls: 16\n", " iterations: 14\n", " root: 1.0297804776674795" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rootval = root_scalar(rootfn, args=(2,), method='bisect', bracket=(0, np.pi/2), rtol=0.0001)\n", "rootval" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle -0.00181398318733272$" ], "text/plain": [ "-0.001813983187332724" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rootfn(rootval.root, 2)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 [0.7390654728477594]\n", "2 [1.0298871106698615]\n", "3 [1.170162999116519]\n", "4 [1.252321886546815, 3.59513706199805]\n", "5 [1.3064634575262268, 3.837259681867517]\n", "6 [1.344703308357839, 3.9856757365803097]\n", "7 [1.373288543385431, 4.088658305156534, 6.616141671133699]\n", "8 [1.3954373678770082, 4.165138006819758, 6.830436280744518]\n", "9 [1.413042843754929, 4.224201538797298, 6.96825118869211]\n" ] } ], "source": [ "allroots=[]\n", "for r in range(1,10):\n", " # calculate the number of roots we expect to find for this radius\n", " n = int(r/np.pi)+1\n", " roots = []\n", " for ii in range(n):\n", " lowrange = ii*np.pi\n", " hirange = (ii+.5)*np.pi\n", " try:\n", " root = root_scalar(rootfn, args=(r,), method='bisect', bracket=(lowrange+0.01, hirange-0.01), x0=lowrange + 0.01, x1=hirange-0.01, rtol=0.0001)\n", " if not root.converged:\n", " print(\"Warning root {} for radius {} did not converge\".format(ii+1, r))\n", " roots.append(root.root)\n", " except ValueError:\n", " print (roots)\n", " print(r, lowrange, hirange)\n", " raise\n", " print (r, roots)\n", " allroots.append((r, roots.copy()))\n", "\n", " " ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "r=1, k=0.7391, α=0.6736, AB factor= 0.6899 E=0.5462 hbar^2/2m\n", "r=2, k=1.0299, α=1.7146, AB factor= 0.3497 E=1.0607 hbar^2/2m\n", "r=3, k=1.1702, α=2.7628, AB factor= 0.1618 E=1.3693 hbar^2/2m\n", "r=4, k=1.2523, α=3.7984, AB factor= 0.0716 E=1.5683 hbar^2/2m\n", "r=4, k=3.5951, α=1.7524, AB factor=-0.1929 E=12.9250 hbar^2/2m\n", "r=5, k=1.3065, α=4.8268, AB factor= 0.0307 E=1.7068 hbar^2/2m\n", "r=5, k=3.8373, α=3.2038, AB factor=-0.0529 E=14.7246 hbar^2/2m\n", "r=6, k=1.3447, α=5.8459, AB factor= 0.0129 E=1.8082 hbar^2/2m\n", "r=6, k=3.9857, α=4.4832, AB factor=-0.0170 E=15.8856 hbar^2/2m\n", "r=7, k=1.3733, α=6.8624, AB factor= 0.0053 E=1.8859 hbar^2/2m\n", "r=7, k=4.0887, α=5.6822, AB factor=-0.0058 E=16.7171 hbar^2/2m\n", "r=7, k=6.6161, α=2.2881, AB factor= 0.1074 E=43.7733 hbar^2/2m\n", "r=8, k=1.3954, α=7.8759, AB factor= 0.0022 E=1.9472 hbar^2/2m\n", "r=8, k=4.1651, α=6.8356, AB factor=-0.0021 E=17.3484 hbar^2/2m\n", "r=8, k=6.8304, α=4.1620, AB factor= 0.0182 E=46.6549 hbar^2/2m\n", "r=9, k=1.4130, α=8.8829, AB factor= 0.0009 E=1.9967 hbar^2/2m\n", "r=9, k=4.2242, α=7.9543, AB factor=-0.0007 E=17.8439 hbar^2/2m\n", "r=9, k=6.9683, α=5.6936, AB factor= 0.0043 E=48.5565 hbar^2/2m\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10,6))\n", "\n", "plt.title('Finite Square Well With Discrete Energies', fontsize=15)\n", "plt.ylim(0, 10)\n", "\n", "\n", "line_color = None\n", "piranges = [(0, np.pi/2), (np.pi/2, 3*np.pi/2), (3*np.pi/2, 5*np.pi/2), (5*np.pi/2, 7*np.pi/2), ]\n", "for xlow, xhi in piranges:\n", " x1 = np.linspace(xlow+0.01, xhi-.01, 200)\n", " y1 = x1*np.tan(x1)\n", " if not line_color:\n", " lines = plt.plot(x1,y1, label='k tan(k)')\n", " line_color = lines[-1].get_color()\n", " else:\n", " plt.plot(x1,y1, color=line_color)\n", "\n", "\n", "plt.xlabel('k', fontsize=15)\n", "plt.ylabel(r'$ \\alpha $', fontsize=15)\n", "plt.grid()\n", "#xmin, xmax, ymin, ymax = plt.axis()\n", "\n", "# Plot the circles\n", "theta = np.linspace(0, np.pi, 100)\n", "for r in range(1,10):\n", " xc = r * np.sin(theta)\n", " yc = r * np.cos(theta)\n", " plt.plot(xc,yc, color='lightgreen', linestyle='dotted', lw=3)\n", " \n", "# Plot the intersections of the circles and the x tan x lines.\n", "scatterx = []\n", "scattery = []\n", "energies = []\n", "for r, roots in allroots:\n", " for root in roots:\n", " k1 = root\n", " alpha1 = k1*np.tan(k1)\n", " scatterx.append(k1)\n", " scattery.append(alpha1)\n", " \n", " abfactor = np.exp(-alpha1)/np.cos(k1)\n", " print (\"r={}, k={:.4f}, α={:.4f}, AB factor={:7.4f} E={:.4f} hbar^2/2m\"\\\n", " .format(r, k1,alpha1, abfactor, k1**2))\n", " energies.append((r, k1,alpha1, abfactor))\n", "plt.scatter(scatterx, scattery, c='red')\n", "\n", "# Plot the asymptotes\n", "ymin, ymax = plt.gca().get_ylim()\n", "xvlines = ( [avline[1] for avline in piranges])\n", "plt.vlines(xvlines, ymin, ymax, linestyle='dashed', color='orange', lw=3)\n", "plt.legend()\n", "\n" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "def fn(x, alpha, k, abfactor):\n", " if -1 <= x <= 1:\n", " return abfactor * np.cos(k*x)\n", " else:\n", " return np.exp(-alpha * np.abs(x))\n" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "def fn2(x, alpha, k, abfactor):\n", " return fn(x, alpha, k, abfactor)**2" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "fnv = np.vectorize(fn)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "N = 200\n", "\n", "xval = np.linspace(-5, 5, N+1)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,5))\n", "r, k, alp, abfactor = energies[0]\n", "\n", "# Normalise the area under the curve\n", "area = quad(fn2, -np.inf, np.inf, args=(alp, k, abfactor) )\n", "yval = fnv(xval, alp, k, abfactor)/np.sqrt(area[0])\n", "#display(exp(-alpha))\n", "#print (area)\n", "\n", "\n", "plt.plot(xval,yval)\n", "plt.title('Wavefunction', fontsize=20)\n", "plt.ylabel('$\\Psi$', fontsize=15)\n", "plt.xlabel('$x$', fontsize=15)\n", "plt.grid()\n", "\n", "ymin, ymax = plt.gca().get_ylim()\n", "xvlines = [-1, 1]\n", "plt.vlines(xvlines, ymin, ymax, linestyle='dashed', color='orange', lw=3)\n", "#plt.legend()\n", "\n", "#plt.savefig('v3p1.png', dpi=200)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$ 3x $" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import display_latex\n", "display_latex(\"$ 3x $\", raw=True)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$ v_0 = 1 \\frac{\\hbar^2}{2m} \\Rightarrow \\Psi = \\left \\{ \\begin{matrix} 0.846 \\, e^{- 0.674 \\, x} & \\text{if } |x| \\lt 1 \\\\ 0.583 \\cos (0.739 x) & \\text{if } |x| \\ge 1 \\end{matrix} \\right \\} $" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$ v_0 = 2 \\frac{\\hbar^2}{2m} \\Rightarrow \\Psi = \\left \\{ \\begin{matrix} 5.166 \\, e^{- 1.715 \\, x} & \\text{if } |x| \\lt 1 \\\\ 1.806 \\cos (1.030 x) & \\text{if } |x| \\ge 1 \\end{matrix} \\right \\} $" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$ v_0 = 3 \\frac{\\hbar^2}{2m} \\Rightarrow \\Psi = \\left \\{ \\begin{matrix} 28.036 \\, e^{- 2.763 \\, x} & \\text{if } |x| \\lt 1 \\\\ 4.537 \\cos (1.170 x) & \\text{if } |x| \\ge 1 \\end{matrix} \\right \\} $" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,5))\n", "\n", "#s = r\"\"\"$ \\begin{{ matrix }}{:.4f} e^{{- {:.4f} x}} & \\text{{if }} x \\leq 1 \\\\ {:.4f} \\sin({:.4f} x) & \\text{{if }} x \\ge 1 \\end{{matrix}} $\n", "s = r\"$ v_0 = %d \\frac{\\hbar^2}{2m} \\Rightarrow \\Psi = \\left \\{ \\begin{matrix} %.3f \\, e^{- %.3f \\, x} & \\text{if } |x| \\lt 1 \" + \\\n", " r\"\\\\ %.3f \\cos (%.3f x) & \\text{if } |x| \\ge 1 \\end{matrix} \\right \\} $\"\n", "#print (repr(s))\n", "eqns = []\n", "\n", "for ii in range(0,3):\n", " r, k, alp, abfactor = energies[ii]\n", " area = quad(fn2, -np.inf, np.inf, args=(alp, k, abfactor) )\n", " #print(r, k, alp)\n", " #print (area)\n", " s1 = s % (ii+1, 1/area[0], alp, abfactor/area[0], k)\n", " #print (alp, np.exp(-alp), abfactor*np.cos(k))\n", " eqns.append((exp(-alp*x)/np.sqrt(area[0]), abfactor*cos(k*x)/np.sqrt(area[0])))\n", " #print (fnv(1, alp, k , abfactor))\n", " display_latex(s1, raw=True)\n", " #display(abfactor/area[0]*sin(k*x))\n", " \n", " \n", " y = fnv(xval, alp, k, abfactor)/np.sqrt(area[0])\n", " #y = fnv(x, alp, k, abfactor)\n", " plt.plot(xval,y, label=r\"$V_0 ={} \\frac{{\\hbar^2}}{{2m}}$\".format(ii+1))\n", " #print (r)\n", "plt.title('Finite Square Well - 1st Energy Level - Various Potentials', fontsize=15)\n", "plt.ylabel('$\\Psi$', fontsize=15)\n", "plt.xlabel('$x$', fontsize=15)\n", "plt.grid()\n", "\n", "ymin, ymax = plt.gca().get_ylim()\n", "xvlines = [-1, 1]\n", "plt.vlines(xvlines, ymin, ymax, linestyle='dashed', color='orange', lw=3)\n", "plt.legend()\n", "\n", "#plt.savefig('v3p1.png', dpi=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now recall:\n", " \n", "$$ \\frac{\\partial \\Psi (x,t) }{\\partial x^2} + \\frac{2m}{\\hbar^2} (E - V ) \\, \\Psi (x,t) = 0 $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Perform a sanity test on the derived equations" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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LG9/W/TZ2HN7BT2vzfmYsYQHQLiJSOIUqKLDWjscVlufe90iur1cBfbwbmoiUiAOL/B0Bby94m7DgMP7c+c8FH5SeBLOvhJ0/QcMroNtrEH6GuqagUGh0BdT/Eyz7J6x+3vVW9R8HFWLyfcnIFiNpULUBr89/nYtaX+TBT+WhAGgXESkczYAuIn51NO0onyz7hEvaXEKtirXyPyj9MEwd6mqjur4KvT87cyKVW3AEdH4O+v0Ih1bDxF6QtDn/Q4OCGdtlLFM3T2XTgU3F+IlEpLxRMiUifvX1qq85nHqYm7oWsKhvehLEnQv758PZX0PL28GY4l2s3igYPA3SD8KUwZCc914a59pO12IwfLzk4+JdR0TKFSVTIuJXny77lKbVm3J2g7NPfTIrA2aOhr1/QJ//QX0vDLvV6gEDJ0DqXpg2zPV65VGvSj2GNh3Kx0s/JuvkGV5ERE6hZEpE/GbH4R1M2zyNqzpchcmvt2nJ/bB7grtTr8El3rtwze7Q73s4vBZmX+UK2/O4ruN1bD20lbgtcd67roiUSUqmRMRvPlv2GRbLVR2uOvXJTZ/Amhehxe3Q7AbvX7z2YOjyEuz8GZY9esrTF7a6kKrhVfloyUfev7aIlClKpkTKu6Y3uq2EWWv5dNmn9KrXi2Y1mp385OH1MP8WiB4AXV7wXRAtboMm18PKJ2FP3ElPVQitwOXtLuebVd+QlJbkuxgK4qd2EZGiUzIlUt71fMdtJWxJ/BJWJq7k6g5Xn/xEVgbMuRqCwqD3p256A18xBrq9CpWbwZxrIO3gSU+PaT+GlIwUfln3i+9iKIif2kVEik7JlIj4xafLPiU0KJRL21568hMrn4J9c6HH21Cxnu8DCYl0Uy2k7IIFt530VJ/6fahTqQ5frfzK93GISKmlZEqkvNu/0G0lKMtm8cWKLzi3+bnUrFjzxBOH18LKJ9yknA0vLfgE3lazO7T9B2z5DHZPPL47OCiYS9pcwvj14zmceupdfz7lh3YRkeJRMiVS3v3WzW0laM72OexO2n1yr5S1brmX4IquMLyktX0QKreA+bdC5rHjuy9rdxmpmaklv7yMH9pFRIpHyZSIlLhvV39LWHAYI1uMPLFzy+ewZyp0eqbApV58Kjgcur8BSRtg5TPHd59V7yzqV6nPlyu/LPmYRKRUUDIlIiXKWst3q79jWNNhVAmv4nZmHIUl90GN7tBsrP+Cqz3YDTGuegaObgMgyARxSZtLmLBhAgdSDvgvNhEJWEqmRKRELdy9kK2HtnJx64tP7FzzEqTshq4vgfHz21Kn7F6ppf84vuuydpeRnpXOD2t+8E9MIhLQlEyJSIn6ZtU3hASFMKrlKLcjZQ+sehbq/Qmi+vg3OIDIBtDyDtjyX9i/GIDusd1pULUBP6z9wb+xiUhAUjIlIiXGWsu3q79lYKOB1KhQw+1c8S/ITDnRIxQI2j4IYdVhyd8BMMYwqsUoJm2cRHJ6sp+DE5FAo2RKRErM8oTlbNi/4cQQ39HtsPFdaHoDVGnh3+ByC6sGbR+G+MmQMAOAC1pdQEpGCpM3TfZvbCIScJRMiZR3wxe4rQT8uOZHDIYLW13odqx61k2J0PbBErl+kTS/GSJiXM8Z0K9hP6qEV+HHNT+WzPVLsF1ExDNKpkTKuxpd3VYCfln/Cz3q9iCmUowrON/4HjS5FiIblsj1iySkIrS+z/VOJc4mLDiMc5ufy8/rfiYzK9P31y/BdhERzyiZEpESsSdpD/N2zjsxt9Sq58BmQJsA7JXK0fxmCI+C5Y8BMKrFKBKTE5m7c66fAxORQKJkSqS8mzvWbT7264ZfATiv+XlwLAE2vAWNroTKTX1+7WILiYTW90L8RDiwhBHNRxASFFIys6GXULuIiOeUTImUdxvfdZuP/bLuF2Irx9KpdidY95pbsqXtQz6/rseajYWQSrD6BapFVKN/w/4lk0yVULuIiOeUTImIz6VlpjFx40RGNh+JyUqF9W9C3ZFQpaW/QzuzsGrQ9C+w9QtI3sGolqNYvXc1G/dv9HdkIhIglEyJiM/N2DqDI2lHOK/FeW4NvtS90PJOf4dVeC3vALJg7X8Y0WwEABM2TvBvTCISMJRMiYjPjVs/jvDgcAY3GgRrX4ZqHSBmoL/DKrxKjaHeRbDhbZpVrk3jao35bcNv/o5KRAKEkikR8blf1v3CoMaDiDwwFw4ud71Sxvg7rKJpfQ+kH8Js/pDhzYYzdfNU0jLT/B2ViAQAJVMi4lObD2xm/f71DG82HNa8DBHR0OgKf4dVdLXOgpo9YP2bDG96DkfTjzJr2yx/RyUiAUDJlEh5V72L23xk0qZJAAyr0xZ2jYNmN0FwhM+u51PNbobDaxgYGUZoUKhvh/p83C4i4j1KpkTKuxEL3eYjkzZNol6VerQ8EOd2NL3BZ9fyuYaXQWhVKm/7lD4N+vDbRh8mUz5uFxHxHiVTIuIzmVmZTNk0hWFNhmA2fQCxIyCygb/DKr6QitD4Wtj+DcMbns2yPcvYdWSXv6MSET9TMiUiPrNw90IOHDvA0Go1IWWXmwCztGt+E2SlMzzsCAATN070c0Ai4m9KpkTKu8+N23wgJ9EYnLoUKtSB2PN8cp0SVbUNRPejQ+JP1K5U23fzTfmwXUTEu5RMiYjPTNo0iS4x7YjaNxWaXA9BIf4OyTuajsUc3czgOu2Yunkq1lp/RyQifqRkSkR84kjqEWZvn83QqtXAZrklWcqK+n+CkMoMCksm4WgCqxJX+TsiEfEjJVMi4hO/b/2djKwMhmZtdLOdV2rs75C8J6QiNLyUQccWAzB181Q/ByQi/qRkSkR8YsqmKUQEh9HH7obG1/g7HO9rfC2NglJoUimKKZun+DsaEfEjJVMi4hNxW+PoXS2KiNAKUP9if4fjfVFnQ6UmDIoMIW5LHJlZmf6OSET8RMmUiHjd/pT9LI1fyoCgfVDvTxBa2d8heZ8x0PgaBpndHEo9xOL4xf6OSET8pIzcWiMixdbjba+fcsbWGVgsA8KPQeOrvX7+gNH4GgYt/j/A1U11i+3mvXP7oF1ExDfUMyVS3jUb6/XJNOO2xBERFESPqjFQe4hXzx1QKjUmpk5f2kaEe79uygftIiK+oWRKRLwubssUekdYwptcWXbmlipIw8sYFJ7KjK3TSctM83c0IuIHSqZEyrsN77jNS/an7GfpnhX0j7DQ8HKvnTdg1R/NoEhDSsYx5u2c573zerldRMR3lEyJlHfzbnKblxyvl6pRG2p4sYYoUFWI4ez6ZwMwY+t0753Xy+0iIr6jZEpEvCpu469EGOjR6kp3x1s5UKvZ1bQJgxkbx/s7FBHxAyVTIuJVcRvH0ysCIhqP8XcoJaf+RfStYJi1c77mmxIph5RMiYjX7E/Zz9ID2xlQtTpU7+zvcEpOeE361enA4Yw0lsUv9Xc0IlLClEyJiNfM2DAOCwxoem65GeLL0bfNtQDMWP1fP0ciIiWtjN+zLCIl6fdVnxBuoEfH2316nawsWLUKFi+GJUtg+3ZISIBDh+DYsS7UqAFRUdCkCTRrBr16QYcOEBzsu5jqt7yeRqF3M33Dz/xt8Iu+u5CIBBwlUyLiNbN2zqNHZAQRtXp4/dzp6TB+PPz4I/zyCyQmuv0VKkCDBhAdDfXqQWJiOhERsH49TJwIKSnuuMqVYcgQuPxyGDkSKlb0coBhVelbox4T9m7CZmVhgtTxL1JeKJkSKe/GWK+cJvnINhYdOcy9zXt7dYhv1y546y147z3YvRuqVYMRI2D4cOjWDVq0gJBc72RxccsZMGAAANa6XquZM2H6dPjpJ/j+e6hUCa67Du66y/VeeUvfRoP5dM/HrNv8Ay2bXuTZybzULiLie/roJCJeMX/FG2QAfVpe4pXzJSTAPfdA06bwxBPQubNLhhIS4PPP4ZproE2bkxOpvIxxvVZjxriEbPt2mDYNLroI3n4bmjeHK66AzZu9EjL92t8MwIyVH3rnhCJSKiiZEhGvmLn+JwB6t/ZsYeOMDHjxRZdEvfyyG5Zbvx7GjYPzz4fQ0OKfOzgYBgyAjz92CdS997phw1at4L774MgRj0KnRWxPokNDmbFtpmcnEpFSRcmUSHn3a1e3eSIjmVkJa2lTqQY1KtYs9mnmz3dDd/fc45KeVavgww9dYuVtdevCs8+6RG3MGHjhBWjXDiZPLv45jTGcHdOa6YcOwpENngXojXYRkRKhZEqkvDuwyG0eyNo9kTkpWfSpd1bxXp8FzzwDvXvD3r3w7bduSK9lS4/CKpS6dV3CNmuWK2YfOhRuvvlE4XpR9Wt+IVsyYPu6jzwLzAvtIiIlQ8mUiHhs1ZqPOZgFfVoUveg6IQGGDYMHH3S1TCtWuMeSnqaqVy831cJ997l6qt69YePGop/n7GajAJi97msvRygigapQyZQxZrgxZq0xZoMx5oECjrnUGLPKGLPSGPO5d8MUkYCVlcmsLZMA6NOwf5FeumwZ9OgBs2e7u/W++MLdrecvFSrAv//t6rO2boWuXeHXX4t2jg4xHagQHMqchHWQssc3gYpIQDljMmWMCQZeB0YAbYArjDFt8hzTHHgQ6GOtbQvc6f1QRSQg7Z3NrCNHiY6oStPqhS9u+ukn1/uTkQEzZsBf/hI4k6afey4sWuSmTTj/fNdTVVihwaF0j+nAnBRg508+i1FEAkdheqZ6ABustZustWnAF8AFeY65EXjdWnsAwFqb4N0wRSRg7fiRWcegT4O+mEJmQx98AH/6E7RuDfPmuR6gQNOokZubatgwV0P14INu3qrC6NVoMIvTIGXrtz6NUUQCQ2GSqbrA9lzf78jel1sLoIUxZpYx5g9jzHBvBSgiAcxa4jd/w6Z0OLvRwEK95MUXXS/UkCEQFwexsb4N0ROVKrketLFjXYH8bbe5Yvkz6VW/N+kWFm6bBhnJvg9URPzKWzOghwDNgQFAPWC6Maa9tfZg7oOMMWOBsQAxMTHExcV56fJlX1JSkv69AlBZaJcWFc8DYF0xfo6K6VvZvncrABGJEWf8t/jsswa8914T+vdP4J57VjN/vvdn+fZFm1x+ORw61IQ33mjA1q27uPvudZxutZisNJdxzUlOo8rkV9gf0avI1/SkXQJRWfhdKWvUJt5TmGRqJ1A/1/f1svfltgOYa61NBzYbY9bhkqv5uQ+y1r4DvAPQrVs3m7Pkg5xZXFwc+vcKPGWjXQYAUKwOotUv8MUqiAgJ54bzbiAsOKzAQ195xRWZjxkDn3wSTXBwdLGiPRNftcmAAW7R5CefjCU2Npa33z59jVeT1Y2Zk7qN+2puh+4PFueKQDHbJQCVjd+VskVt4j2FGeabDzQ3xjQ2xoQBlwN5qyp/IPs33xhTCzfst8l7YYpIQNr1K3+kV6BbbPfTJlLvvQd33unqpD7+2M1EXtoY45a1eeghePddePjh0x/fq35v5qSGYHf8UvhiKxEplc6YTFlrM4DbgAnAauAra+1KY8y/jDGjsg+bAOwzxqwCpgH3WWv3+SpoEfGi/QvdVlTpR0hL+J1FKWn0rNuzwMO++srVHA0fDv/73+nX0isNnngCbroJnn7azZpekF71ehGflsrWw9vh0KqiX6i47SIiJa5Qb2vW2vHA+Dz7Hsn1tQXuzt5EpDT5rZt7HFPE3pM9U1mWkkFqFgUmU7NnuwWJe/eG776D8HAPYw0AxsDrr8P+/W5tv6go9zPm1au+q5Oacwwa7RoH1doW7ULFbRcRKXGaAV1EimfXeOamueyoZ71Tk6mNG+GCC6B+ffjhBzchZlkRHAyffgqDB8MNN7ilaPLqENOBiqEVmWNrwa5xJR+kiJQYJVMiUnTWwq5fmWtiqF2pNvWr1D/p6QMH4Lzz3DQC48dDrVp+itOHwsPh66/dfFR/+hNs2XLy8yFBIXSP7c6c1FBInAVpB/wRpoiUACVTIlJ0h1ZC8nbmHk2lZ92eJ03WmZkJV1wBmzbB999D8+Z+jNPHqleHn3+G9HQYNQqSkk5+vnf93iw5nEByZibsnuSfIEXE55RMiUjR7RrPgUxYd2TPKfVSjz0GEybAa69Bv35+iq8EtWzpiuxXrYJrrz35xr1e9XqRkZXJgqwqGuoTKcOUTIlI0e36lXkhjYGT66V++QUefxz+/Ge48UZ/BVfyhg6FZ591Rfavvnpif4+6PQCYH9IUdv8GthDTp4tIqaNkSkSKJv0wJM5kblBdDIZuse6us02b4OqroXNnd7dboCxaXFLuvtsV3N97L/zxh9sXUymGBlUbMC8tFI4lwMHl/g1SRHxCyZRIeTd8gdsKK34y2AzmJmfQOqo1VcKrkJYGl13mnv7mm7J1515hGQMffgj16rl/i33ZM+11j+3O/IPx7pvdEwt/wqK2i4j4jZIpkfKuRle3FdauX7EhVZibuP54vdSjj8KCBW6m8yZNfBRnKVC9urvDLz7eDXVa64b6Nh/axt6KrSC+CMlUUdtFRPxGyZSIFJ61sHsim6qexb6UffSs25Np01y90A03wMUX+ztA/+vWzf17/PwzvP++65kCmB/eGhJmQEaynyMUEW9TMiVS3s0d67bCOLIBkrcxN6guAK0q9+Tqq930By+/7LsQS5u//c1N6HnnnVDtWFcMhvmZlSAr1SVUhVGUdhERv1IyJVLebXzXbYUR7+ZKmpuSScXQirz+aDsSEuDzzyEy0ocxljJBQfDRRxAaCrf+pQqtarVi/qG9EBRW+KG+orSLiPiVkikRKbz4yRDZiLkJa2kU1pWvvwzhkUegq0p7TlGvHrz5JsyZA+H7ujNv90JsrbOPJ6QiUnYomRKRwsnKgD1TSY0eyOLdi9kyqyedO8P99/s7sMB1+eVuW/ZbdxKOJrC9Wg83PULKbn+HJiJepGRKRApn/wJIP8SysGakZaVxbENPPvjADWVJwV59FSodcpN3zs2s6XZqaRmRMkXJlIgUTvxkwPDp0jAAbv1TNzp18mtEpUJUFLz8QEfIDOXtuAQIjyraFAkiEvCUTIlI4cRPIrNKZ96ftIbg1Bo893BDf0dUalx3VThVUjowbe0CjlYe6uqmtLSMSJmhZEqkvKvexW2nk54Ee+cwbc0QkqsupFvdboSHl7P1YjxgDIzq2oOs2gt446ch2UvLLDv9iwrTLiISEJRMiZR3Ixa67XQSpkNWOk//tz9BtVcwqJVu3yuqQS27Q/gR/j0+e4r4M9VNFaZdRCQgKJkSkTOy8ZNJzQhnpalElsk4vrixFF73um4m9EodtrIhoSUZu6b5OSIR8RYlUyJyRgdWT2L66r6c85eVAHSto56pompdqzWRoZF0u2A+k5YNJHP3DMhK93dYIuIFSqZEyrvPjdsKsG9nPDWCVrDx6BCC6y+gZoWaNKjaoAQDLBuCg4LpGtuVbZnzIGYQ4cFJbFl8mmG8M7SLiAQOJVMiclrfvemGo4ZcNZhFuxfSLbYbxuiPfHF0q9ONpfFLueCWPgBM/Xwq1vo5KBHxmJIpESnQkiVg4+NIyahC3Y6tWJGwQkN8HuhSpwupmansC9/H3oz21A+bxvff+zsqEfGUkikRyZe1cPfdMKhtHCGx/ViWuJJMm6nicw90qeOmOli0exE1Wg+kb6uZ3H9vKseO+TkwEfGIkikRydfPP8OaxbtoFrOO0LoDWLjb1fd0jVXPVHG1qNmCyNBIFu1eRFCdQUSEHqNO+FxefdXfkYmIJ5RMicgp0tLg3nthzJA4tyNmIAt2LaBWxVrUr1Lfr7GVZsFBwXSq3cklptH9AMPNF07lySdh715/RycixaVkSkRO8cYbsH49/O2yOAitCtU6slDF517RpU4XlsQvITOkCtTowgW9pnH0KDz2mL8jE5HiUjIlUt71eNtt2fbvh3/9C4YNg/rhcRDdj5TMNFYmrFTxuRd0qdOFo+lHWb9/PcQMJDL5D/56UzJvvQVr1+Y6ME+7iEjgUjIlUt41G+u2bE89BYcOwctP78QcWQ/RA1i6Z6mKz70kdxE6MYMgK43HbptNRAQ88ECuA/O0i4gELiVTInLcjh3w2mtw9dXQusbvbmfMABbuyi4+V8+Ux1rXak14cLhLpqLOBhNM9bRpPPAA/PADTJ/u7whFpKiUTImUdxvecRtueC8rC/7v/4A9ccfrpRbsXkBUxSjqVannz0jLhNDgUDrW7uiSqdDKULMHxE/lrrsgNhYefNBNS5G7XUQksCmZEinv5t0E825i3Tr44AO4+WZo1AhIiHN3nAUFs2j3IrrGdlXxuZd0qd2FRbsXYa2FmIGwfz4VQ5N45BGYPRvGjeN4u4hI4FMyJSIAPPIIRETAww8DyTshu14qNSOVVYmr6Fy7s79DLDO61OnCodRDbD64GaL6gc2EfX9w/fXQtGl2G4hIqaFkSkQA+PJLuOsuiIkBEk7US61MXElGVgadanfyZ3hlyklF6FG9wARBwnRCQ91Q67Jlfg5QRIpEyZSIAFCjhpuoEzipXmpJ/BIA9Ux5UbvodoQEhbjC/tAqUL0zJLjK88svh/bt/RygiBSJkikRAWDsWKhaNfubXPVSS+KXEBkaSdMaTf0ZXpkSHhJOu+h2LIpf5HZE9YN9cyEzlaAgeOgh/8YnIkWjZEqkHLP2xNf33Zf9Ra56KYDF8YvpWLsjQUZvF950UhF6dF/IPAb7FwBw6aUnjtMiyCKBT++OIuXYhAknvq5RI/uL4/VS/cmyWSyNX6ohPh/oGtuVvcl72XF4h5tvCo4P9QXlemd+6y0/BCciRaJkSqScshb+8Q9o9JAlbXSuLqrEmRBSGap1YvOBzRxJO6Licx/IKUJfuHshRERB1TaQMOPEAWMsQz6wPPUUHDnipyBFpFCUTImUUz/8AAsXwqOPQlhYricSZkBUbwgKZnH8YkDF577QIaYDQSboeIE/Uf1cIpuVefyYp56CxER4+WW/hCgihaRkSqQcyshwRc4tW7qlY45LOwCHVhwfdloSv4RgE0zb6Lb+CbQMqxhakeY1mrN0z1K3I7ovZByBg0uPH9OjB1x4ITz/POzb5584ReTMlEyJlEMffQRr1sDTT0PIpK7wa/aae4mz3WNUX8AVn7eJakNESIR/Ai3jOtXulKtnyv2b59RN8atrl8cfd8N8zz7rlxBFpBCUTImUM8nJbmjvrLNcrwcHFrkNIHEGBIVCze6A65lSvZTvdIzpyJaDWzh47CBE1ofIxq4N4Hi7tGsHV14J//kP7Nrl13BFpABKpkTKmVdfdX+Un30WTllqL3EmVO8KIRVJOJrAriO7lEz5UM6/7bI92VOeR/d1PVO556wAHnvMDc3+618lHKCIFIqSKZFyZP9+eOYZGDkS+vXL82TmMdg33/1BB818XgI61u4IwNL4nLqpfpC6Fw6vOem4Jk3cAtTvvQerV5d0lCJyJkqmRMqRp5+Gw4fd4yn2zYestJOKz+HEH3zxvjqV6lCrYq0TRehR2Rlu4oxTjn3kEYiMhPvvL8EARaRQlEyJlBPbtrm6m2uvhXbt8jkg5w94VB/AFZ83rNqQGhVq5HOweIMx5uQi9MrNIKL2iSL0XKKi4MEH4eefIS6uRMMUkTNQMiVSTvzjH+7xsccKOCBhpps4MrwmoOLzktIxpiMrElaQkZXhitii+56YhT6PO+6A+vXdgtRZWSUcqIgUSMmUSDkwbx58+incfTc0aJDnyaY3QpMbYO+s40N8R9OOsnbvWtVLlYCOMR1JzUxl7d61bkdUX0jeAQ2vcG2TS4UKbiLPhQvhf//zQ7Aiki8lUyJlnLVw110QE+OGiU7R8x1oeRukHz4+19HyhOVYrHqmSkDOv/GJuqnsdfrqjnRtk8eYMdCli5t0VYsgiwQGJVMiZdxXX8Hs2fDkk1C5cgEHJc50j3mKz5VM+V6rWq0ICw47cUdftfYQUgkSZ+V7fFCQmxF92zZ45ZUSDFRECqRkSqQMS0mBv/8dOnWC664r4KD9C2HHj1CxHkQ2BGDx7sVUj6hOg6p5xwTF20KDQ2kb1ZYle5a4HUEhUKsX7J7o2iYfAwfC+ee7BDk+vuRiFZH8KZkSKcNeesn1YLz0EgQHF3DQb90gfpLrlcqexXPJHld8bk6Z1VN8oWPtjid6psDdUZm0wbVNAV58EVJTCxi6FZESpWRKpIzavdsVK//pTzBgQCFekF0vlZmVyYqEFXSM0fxSJaVjTEf2HN1DfFJ2N1NO3dRpNGvmauE++gjmzvVtfCJyeoVKpowxw40xa40xG4wxD5zmuIuNMdYYU/DHKREpEQ8+CGlp8NxzhXxBZCMANh3YRHJ6Mh1iOvgsNjnZ8SL043VThbuL8uGHoU4duP12TZUg4k9nTKaMMcHA68AIoA1whTGmTT7HVQbuAPQZScTPZs2Cjz+Ge+6Bpk0L+aLaQ4ET68QpmSo5Ob2Ax+/oiyjcRKmVK8O//w3z58Mnn/gqOhE5k8L0TPUANlhrN1lr04AvgAvyOe5x4FlAN+uK+FFGBtx6q5vcMWeizkIJDgXctAhBJog2Uad8ZhIfqV6hOvWr1D8xE3pumamnfe2VV0KvXvDAA3DokG/iE5HTK0wyVRfYnuv7Hdn7jjPGdAHqW2vHeTE2ESmGN9+EpUtd0Xlk5BkOPpZ4yq5le5bRvEZzKoRW8E2Akq9OtTud6JnKbd/8077OGHj1VUhIgH/9y0fBichphXh6AmNMEPAicF0hjh0LjAWIiYkhTgtMFVpSUpL+vQJQoLXL/v2hPPhgT7p1O0yNGsvOuIZbrZSZ5CzTl/NzzN0yl+aVmwfUz1UUgdYmhVXtWDXWJK5hwpQJhAeHMyB7/6a5H7GtcsYZX3/uuS14+eU6tG27gCZNjvo01uIore1SlqlNvKcwydROoH6u7+tl78tRGWgHxGXfRl0b+MkYM8pauyD3iay17wDvAHTr1s0OKNQtRgLuD53+vQJPoLXLdde5ovPPPqtBixYDzvyCRT/DwVAY8jsDonqRlJbErt93cUuvWxjQrxCvD0CB1iaFtS96H59u+5SarWvSLbYb7F8AMy+jSaUdNCnEz9O+PbRqBe+/350ZM9zknoGktLZLWaY28Z7C/LrNB5obYxobY8KAy4Gfcp601h6y1tay1jay1jYC/gBOSaRExLdmznRF5/feCy1aFPJFCTMgqpfbgBUJKwAVn/tDx9quCP143VSNrlDnHDcTetaZe6Zq1nQzo8+eDR984MNAReQUZ0ymrLUZwG3ABGA18JW1dqUx5l/GmFG+DlBEziw9HW65xRWdP/xwYV+UBAcWHZ9fCnQnnz81qd6EyNDI420AuLbJSIIDSwp1jmuugf793az3iaeWw4mIjxSqI9haO95a28Ja29Ra+2T2vkestT/lc+wA9UqJlKznnoMVK+D11wtRdJ5j3x9gM2H/Ipg7FoDle5ZTOawyDas29F2wkq8gE0S76HYsT1judswdCzt/dl8nTC/UOYxxNyAkJcF99/koUBE5RYCNqotIUa1f7+7iGj3arddWaAnTwQTB7l9h47sALEtYRvuY9lpGxk86xHRg2Z5lWGtdm2z9HCo1hcTCJVMArVu7ROrjjznjDQgi4h1KpkRKMWvhppsgIsLdHl8k8VOgRvdc57Is27OMDtEa4vOX9tHt2Z+yn91Ju0/sjO7natts4ac4f/hhaNwYbr4ZjmnmPxGfUzIlUop99BFMm+Zmwa5TpwgvTD8C++ZB7cHHd+04vIODxw6qXsqPcv7tl+9ZfmJndD9I2w+HVhX6PBUruuG+tWvh8ce9HaWI5KVkSqSUSkhwy8X07Qs33FDUF88AmwExg47vUvG5/7WPaQ9wchF6dD/3WMi6qRznnAPXXgvPPguLF3srQhHJj5IpkVLqjjvg6FF4++1izCm0ZyoEhUOt3sd35fwBbxfdrqBXiY/VqFCDupXrnihCB4hsDBXqwp5pRT7fiy9CrVpw/fXujk8R8Q0lUyKl0PffwxdfuLX3Wrcuxgn2TIWo3hByYsmY5QnLaVi1IVUjqnovUCmy9jHtT+6ZMsYNx+6ZWqS6KYAaNeCNN2DJEjcHlYj4hpIpkVJm715XWNyli1vctshS97l5i3KG+Kp3gepdXPG5hvj8rkN0B1bvXY2t3tm1DUDtoa5u6kDRx+suugguvhgeewzWrPFysCICKJkSKXVuvx0OHHDF56GhxTjBnjjAnkimRiwkdehs1uxdo2QqALSPaU9aZhqrun4KIxa6nbWHuMfdk4p1ztdec0Xp118PmZleClREjlMyJVKKfPutG9575BG3Flux7JkKIZWg5olpEVbvXU2mzVQyFQDaR7uGPaluqkJtqNYe4icX65y1a8Mrr8CcOfDCC96IUkRyUzIlUkokJrolY7p0gfvv9+BEe6a4O8SCTnRr6U6+wNGqVitCgkJOnh4BIGYIJM6EjJRinfeqq9yQ3z//CcuWnfl4ESk8JVMipYC1cOutcPCgm9m6WMN7AMk74fDak6ZE4HPDNSuvJSIkgmY1mnkjXPFAeEg4LWu25Mk9T8HnuWairzMUslIhcUaxzmsMvPUWVKsGV18NqaneiVdElEyJlAqffgpff+2KiNt5MnNBzu31uSbrzNEmqg0hQSEenFy8Jd8ewuh+EBRW7KE+gKgoePdd1zP12GMeBCgiJ1EyJRLgNm+G225zk3P+/e8enmz3BAivBdVO/WOtIb7AkVM3dZKQSDcvWHzxitBzjBrlCtGffRZmz/boVCKSTcmUSADLyHC1Lsa43qngYA9OZrNg929QZ7hb4DgPrckXOApMbGsPcdNaHEv06PwvvQT168M118CRIx6dSkRQMiUS0J5+2vUevPEGNGzo4cn2LYDUvRA7It+nm9Zo6uEFxFtaRxUwE2vtoe4xfopH569SBT75xPV63nqrR6cSEZRMiQSsuXNdXcsVV8CVV3rhhLvGAwbqnJPv0yo+DxyNqjbK/4kaXSG0GsRP9Pga/fq5O/s+/dRtIlJ8SqZEAtDhw254r25d1yvlFbt/hZo9Ibxmvk+3iWrjpQuJp4IKWmwxKBjqDINdvxZ5aZn8/OMfrhbvlltg/XqPTydSbimZEgkw1sJNN8GmTfDf/7pb2T12LBH2zYfYc0956oljDXg5qzgL/IkvfVFxILfvDSMrb9JUdyQci4f9izy+RkgIfPYZhIXB5ZdrugSR4lIyJRJg3n3XzXL++OOu18Ardk8A7Cn1UhlZGTyxaw87ok9NssS/jja4ktcOpLHpwKaTn6gzwt1AsPMXr1ynfn348ENYtAgefNArpxQpd5RMiQSQZcvgjjtg2LBiLmJckF3jISIaanQ5aff6fetJzUzVtAgBqGPtjgAsjV968hMRtaBWL9jlnWQK4IILXCH6Sy/B+PFeO61IuaFkSiRAJCXBpZdC9equILigspkiy8p0PVP5TImwbM8ybqwCAzNUMBNoOhz5g5uqGpbELzn1ydiRsH8hJO/y2vWefx46dIBrr4UdO7x2WpFyQcmUSACw9kQR8OefQ3S0F0++bx6k7c+3XmpJ/BLeiYH6a5/w4gXFG8IW3s5b0Zale5ae+mTdke5x1zivXS8iAr78Eo4dg0sugbQ0r51apMxTMiUSAN580xWbP/ooDBjg5ZPvGud6pHLmKMplUbznRcziW/kmU1XbQmRDr9VN5WjVytVP/fEH3H23V08tUqYpmRLxs1mzXJ3UyJHuVnWv2/EDRPWF8Bon7bbWsmi3kqlAt+3QNvan7D95pzFuqC9+MmSkePV6o0fDvffC669r/imRwlIyJeJHu3a5P16NG3u5TirH4XVwaCXUv+iUp3Yc3sHe5L1evqD4wrI9y07dWXckZCZDQpzXr/f0066HdOxYWLLE66cXKXOUTIn4SVqaq005cgS++85L80nlteN791jvwlOeUq9U6XHKHX0AMQMguCLs/Nnr1wsJcdNz1KwJF18MBw54/RIiZYqSKRE/ufNOt+7eBx9Au3Y+usj276FGN4hscMpTi+MXE5TPgscSWGIiY1gcv/jUJ4Ij3NJAO370ymzop1w3Br7+GrZvh6uvhizvX0KkzNA7qYgffPihKzq/7z43HYJPJO+AfXOh/p/yfXrR7kW0qtXKRxcXb+ka25UFuxbk/2SD0ZCyC/bO8cm1e/WCl1+GcePcOn4ikj8lUyIlbM4cNw3C4MHw1FM+vND2H9xjvVPrpcAlU13qdIEx1m0SWLLbpXtsd1bvXU1SWtKpx9QdCUHhsO1rn4Vxyy2uduqpp1SQLlIQJVMiJWjLFjfbdL16riYlJMSHF9vxPVRpDVVP7X3ak7SHnUd20qV2l3xeKIGke2x3smxW/jVuoVXcUN/2b30y1AfuxsHXXnMF6Tfc4IamReRkSqZESsihQ276g/R0N2xSq5YPL5a6DxJ+L3CIL6cGp0sdJVOBrnvd7gDM3zk//wMajHZDunvn+iyG0FD45hto0AAuvBC2bvXZpURKJSVTIiUgIwMuuwzWroVvv4WWLX18wZ0/g83Md0oE4HgNTqfaneDXrm6TwJLdLtGR0TSo2oAFuwuom6o7CoJCYfs3Pg2nZk34+Wd3F+rIke4uVBFxlEyJlIA774QJE1zR+aBBJXDBbV9DxQZQPf+ep7k759KqViuqRlSFA4vcJoElV7t0i+1WcM9UWFWoPQy2fePWJfKhVq3cHX6rV8OYMZCZ6dPLiZQaSqZEfOw//3GzSd93n6s58bljiW5h40ZXuIKXPKy1zN0xl7PqnVUCwYg3dI/tzsYDG0+dCT1Hg0sgeRvsKyDh8qKhQ+GVV+CXX9yHBB/nbyKlgpIpER/68Uf3B+fCC+GZZ0rootu+dkN8Dcfk+/Tmg5tJTE7krLpKpkqL7rGubqrAKRLqlcxQX45bb3Vr9732Gjz7bIlcUiSgKZkS8ZEZM+Dyy6F7d7eIsdeXiinI1s+hajuo3iHfp//Y8QeAeqZKka6xrqatwGQqrLpbyHrrlz67qy+v556DK66ABx+ETz4pkUuKBCwlUyI+sHw5nH8+NGrk7tyLjCyhCydtgcRZ0Cj/XilwyVRkaCRto9uWUFDiqWoR1WhZs+XxRDhfja50Q30J00skpqAgN/ns4MHwl7/Ab7+VyGVFApKSKREv27IFzjkHKlVyRec1a5bgxbf+zz02vKLAQ/7Y8Qfd63YnJMiXk1yJt/Wu35vZ22djCypSqnchhFSCzSU3s2Z4uFtXsl07t2D3fN+XbIkEJCVTIl6UmOgSqZQU90m9walL4vmOtbDlM4jqA5Ua5XvIsYxjLIlfQs+6PU/sbHqj2ySw5GmXPvX7sC9lH+v2rcv/+JCKrhB929eQkVxCQUKVKjB+PERFwXnnwfr1JXZpkYChZErES5KS3B+TbdvcfDw+W7y4IAeXw6GVBRaeAyzevZj0rPST66V6vuM2CSx52qVPgz4AzNo+q+DXNL4GMo64xY9LUJ067sODtTBkiCb1lPJHyZSIFyQnu4kMFy2CL7+Es8/2QxBbPgMTAg0KXjk5p+bmpJ4pKRVa1mxJzQo1mbXtNMlUdD83v1gJDvXlaNkSJk50M/0PGQK7d5d4CCJ+o2RKxEPHjrmpD2bMcAvBjhrlhyCyMmDzJ1BnOEQUvE7NjG0zaFytMXUq1zmxc/9Ct0lgydMuxhh61+99+p4pEwSNr4L4CZASXwJBnqxzZ9dDFR/vEqrExBIPQcQvlEyJeCA93XDxxTBpEnzwgbtV3C92jYNj8dCs4NqnLJvF9K3T6d+o/8lP/NbNbRJY8mmXPvX7sHbfWvYm7y34dY2udtMjbPncxwHm76yz3ISemza5+sGDB/0ShkiJUjIlUkzp6fCvf7Vh/Hh4+2249lo/BrPhPahQB2LPLfCQ1Ymr2Zeyj34N+pVgYOJNOXVTs7fPLvigqq2gZg/Y/LHfpifv3x++/x5WrIARI7SOn5R9SqZEiiEjA666CmbOjOLVV2HsWD8Gk7wDdo+HJn+G00x3MH2rm3/olJ4pKTW6xXYjNCj09HVTAE2uh4PLYN+8kgksH8OHw1dfuekSRoyAo0eD/RaLiK8pmRIpovR0l0h99RXcfPNGbr/dzwFt+sgN6zS5/rSH/b71d+pWrkvjao1LJi7xuoiQCLrX7c7vW38//YGNxrg5pza8VTKBFeDCC+GLL2DuXLjvvo4a8pMyS8mUSBGkpsIll7g79p57Di67bLt/A7JZsPF9iBkElZsWfJi1TN86nX4N+2HyWfxYSo9BjQaxYNcCDqceLvig0MrQ6CrY+gWkHSi54PIxejR88w2sX1+JIUNgfwFrNYuUZkqmRAopORkuuMAtXvzaa3Dvvf6OCIifAke3nHHSzY0HNrI7aTf9G2qIr7Qb1HgQmTaTGVtnnP7A5jdB5jHY5P+F8y64AB5/fAUrVsCgQbrLT8oeJVMihZAzIefEifD++3Drrf6OKNvGdyGsBtS/8LSH/b7FDQv1a6ji89KuV/1ehAeHM3Xz1NMfWL0T1Ozphvr8VIie21ln7eenn2DtWhg40E2fIFJWKJkSOYODB2HYMDeP1GefwfWnL00qOUe3w/bvXOF5cMRpD526ZSrRkdG0qtXq1CeHL3CbBJYC2iUiJII+DfowdcsZkimA5jfD4TWQeIZerBIybJhbembzZujb1z2KlAVKpkROY9cud5v3ggWu4Nxv80jlZ/0bgIUWt532sCybxeRNkxnaZGj+9VI1urpNAstp2mVgo4EsiV/CvuR9pz9Hg0shtBqsf9P78RXTwIEweTLs2we9e8OyZf6OSMRzSqZECrB2rXuz37QJxo2Diy7yd0S5ZCTDhneg3oUFLmqcY9meZSQcTWBY02ElEpr43qDGgwCI2xJ3+gNDKkKTa2H7t5C80/eBFVKvXq6nNzgY+vWD6dP9HZGIZ5RMieTjjz+gTx9ISYHff4ehQ/0dUR5b/gtp+6HlHWc8dOLGiQAMaTIk/wPmjnWbBJbTtEv32O5EhkYyZfOUM5+n5d/AZsK6/3g5QM+0bQuzZ7tFkocNczd2iJRWSqZE8hg3zt1xVL26e7Pv0sXfEeVhLax91RUYR/U94+GTNk2iXXQ7YivH5n/AxnfdJoHlNO0SGhzKgEYDmLBxAvZMxeWVmkC9i2D925Ce5INAi69BA9dD1amT6/l9V/8bSilVqGTKGDPcGLPWGLPBGPNAPs/fbYxZZYxZZoyZYoxp6P1QRXzvvffcbdxt2sCsWdC04Kmb/GfPFDi0ElreCWeYMyo5PZkZW2cwrImG+MqaEc1GsOnAJtbvX3/mg1vfA+kHYdMHPo+rqGrVgilTXO/U2LFw//2QleXvqESK5ozJlDEmGHgdGAG0Aa4wxrTJc9hioJu1tgPwDfBvbwcq4kuZmW7eqBtvdEN6cXEQHe3vqAqw5mWIiIaGl5/x0BlbZ5Camap6qTJoRPMRAPy6/tczH1zrLKjV2/2/k5Xh28CKITISfv4ZbrkF/v1vNzFucrK/oxIpvML0TPUANlhrN1lr04AvgAtyH2CtnWatzflf/w+gnnfDFPGdI0fcshcvvAC33+7e1CtV8ndUBTiwFHaNg+a3QXD4GQ+fsHECYcFh9G145uFAKV2aVG9Cq1qtGL9hfOFe0PoeOLoZdnzv28CKKSQEXn8dXnrJLZLcvz/s3u3vqEQKpzDJVF0g95oZO7L3FeQvQCE+Kon439atrtD811/dG/mrr7o39YC18ikIqQwtTz8dArglZH5e9zODGg+iYmjFEghOStq5zc7l9y2/czTt6JkPrnsBVGoKq58PiEk882MM3HmnK0ZfvRp69tTUCVI6ePXPhjHmKqAbkO+aFcaYscBYgJiYGOLi4rx5+TItKSlJ/15etnJlFf75z3akpQXxzDMradPmAEX9Jy7JdqmYvo3uiV+zrdIVbJ699IzHb0vexob9GxhZc+RpYxyQ/VhW/v8qK78rA7IfT/ezxCbHkpqZyqs/v0qvmr3OeM7Y4PNpse9llk58kQPhJTu3WFHapXJleOmlSjz0UHt69gzh/vvXMGCA1qDxtrLyuxIQrLWn3YBewIRc3z8IPJjPcUOA1UD0mc5praVr165WCm/atGn+DqHMyMqy9o03rA0NtbZpU2tXry7+uUq0XWZfa+0XFaxNSSjU4c/OfNbyf9jth7af/sDxXdxWRpSZ35VCtMux9GM28slIe8svtxTunBnHrP2urrUT+7hfhBJUnHbZudPaXr2sBWvvv9/ajAzvx1WelZnflRICLLAF5DSFGeabDzQ3xjQ2xoQBlwM/5T7AGNMZeBsYZa1N8FKeJ+J1KSluOZi//hWGDIH586FVPiusBJykzW5uqWZjISKqUC/5ae1PdKnThXpVzlDCOGKh2ySwFKJdwkPCGdp0KD+t/YksW4hb4ILDoe1DkDjL3RUa4GJj3c0gN98Mzz4L557rZk4XCTRnTKastRnAbcAEXM/TV9balcaYfxljRmUf9hxQCfjaGLPEGPNTAacT8ZstW+Dss+Gjj+CRR+CXX9xcUqXCqn+DCYbW9xbq8MSjiczePpvzW5zv48DE3y5qdRE7j+xk/s75hXtB079Ahbqw/LGArZ3KLSwM3nzTzUEVFwfdusGSJf6OSuRkhZpnylo73lrbwlrb1Fr7ZPa+R6y1P2V/PcRaG2Ot7ZS9jTr9GUVK1oQJ0LUrbNzo7tZ77DEIKi1T1iZtgk3vuwWNKxbuRtnx68djsYxqqV/Fsm5ki5GEBIXw3ervCveC4HBo+yAkzoQ9hVgsOUDccINbdiY93S1H8+67pSIXlHKitPw5ESmW9HR44AEYPtwNGSxYACNH+juqIlr2iOuVavfPQr/kuzXfUa9KPTrX7nzmgz83bpPAUsh2qV6hOoMbD+a7Nd+deTb0HMd7px4tVRlJz56wcCH07esm+BwzBg4f9ndUIkqmpAzbvNktovrss+6Nd+5caNbM31EV0YGlsOVztwZfxdPNSHLCwWMH+W3Db4xuPRpzhhnSpWy4qPVFbNi/geUJywv3guCIE7VTu8b5Njgvi4mB336DJ56Ar75yPc6LF/s7KinvlExJmfTNN9C5M6xa5d5w334bKpbGqZaWPgShVaHN/YV+yY9rfiQtM43L2l3mw8AkkFzQ8gIMpvBDfQDNboTKzWHx3wNyVvTTCQqChx92NVQpKXDWWfDaa6Wqk03KGCVTUqYkJcFNN7nlKFq1coWql1zi76iKKWE67BoPbR+AsMJXyn+58ksaVm1Iz7o9fRicBJKYSjH0bdiXr1Z+VfihvqBQ6PQsHF4NG9/3bYA+0rev+x0fMsStXnDeeZo1XfxDyZSUGbNmQceOrjD17393q9E3buzvqIrJWlh8P1SIhRa3F/pl+5L3MWnTJC5te6mG+MqZK9pdweq9q1kSv6TwL6p3IUSd7Wqn0o/4KjSfqlXL3Zn72mswbRq0bw/ffuvvqKS8UTIlpV5qqltpvm9fl4PExbk6qdBQf0fmgS3/hX1/QIfHIaTw45Pfr/mejKwMLmurIb7y5pI2lxAaFMp/l/238C8yBjo/D8f2wOrnfBecjxkDt97qaqcaN4bRo+Haa+HQIX9HJuWFkikp1ZYuhe7d3UrzN9zgvu/Xz99ReSj9MCy+D2r2gCbXFemlny//nGY1mtGlThffxCYBq2bFmpzb/Fz+t+J/ZGZlFv6FtXpCg8vcmn1Ht/kuwBLQqhXMnu3mkfvsM+jQASZO9HdUUh4omZJS6dgx+Oc/3QR+iYkwbhy8845b06vUW/4vOJYA3V4DU/hf0c0HNjNtyzSu7Xht0Yb4erztNgksxWiXqzpcxe6k3UzbMq1o1+r8rHtceEfRXheAQkPdPHIzZ0KFCnDOOfDnP8P+/f6OTMoyJVNS6syYAZ06uVujx4yBFSvcMhNlwqFVsPYVNw9Qze5FeunHSz/GYLi247VFu2azsW6TwFKMdhnZYiRVwqvw6bJPi3atyIbQ/lHY8QPs/KVorw1QZ53litMfegg+/RTatFEtlfiOkikpNQ4dgltuccN4qaluVvOPP4aaNf0dmZdYCwv+BiGVoONTRXppls3ioyUfMaTJEOpXre+jACXQRYREcGmbS/lm1TccOlbEgqGWd0HVNrDgdshI9k2AJSwiAp580q3BWaeOq6UaPRp27vR3ZFLWKJmSgGctfPGF+2T5zjtw992uN2rYMH9H5mWbPnKLz3Z8stCLGeeYtnkaWw9t5c+d/lz06254x20SWIrZLmO7jiU5PZnPln9WtBcGh0H3N+HoFljxRJGvG8g6d4Z58+Dpp92df61awQsvuBUSRLxByZQEtBUrYNAguOIKqF0b5sxxb4KRkf6OzMuSd8GiuyCqLzS/ucgv/2DJB1QNr8qFrS4s+rXn3eQ2CSzFbJdusd3oXLszby98u/BzTuWI7geNr4U1z8OBZUW+diALDXVLS61c6Xq3773XJVm//+7vyKQsUDIlAenQIbjrLlcbtWwZvPWW+2TZo4e/I/MBa2H+zZCVCj3fL1LROUB8Ujxfr/yaazpeQ4XQCj4KUkoLYwxju45l2Z5lzN05t+gn6Py8myT2j2shM837AfpZ06aud+qHH9wkvwMGwNVXQ3y8vyOT0kzJlASUrCxXB9WiBbzyipvuYN06N6t5cLC/o/ORrV/Azp+hwxNQpXmRX/7uwndJz0rnth63+SA4KY3GtB9DZGgkby8sxl2aEbWgx7twYAmsLFvDfTmMgQsucMtN/eMfbsmpli3huefcncIiRaVkSgLG1KluzqjrrnMT782b53qkykyBeX6Sd8HC26FmT2h5Z5Ffnp6ZzlsL3+KcpufQomYL78cnpVKV8Cpc2f5KvljxBYlHE4t+gnqj3HDfyqdg33zvBxggKlaExx935QR9+7qVE1q3djWaWudPikLJlPhdztQGgwfD3r3wySdu4r1u3fwdmY9lZcKcqyAjBc76CIKK3vX23erv2HVkl3ql5BR3nnUnxzKO8eaCN4t3gq4vQ4U6MOca9/9oGda8uRv6mzwZqlZ1NZpnneXmqhIpDCVT4jc7d7phvI4dXfL073/D2rWufiGoPPyfufrfsGcadPsPVG1V5Jdba3ll7is0qd6EEc1G+CBAKc1aR7Xm3Obn8vr81zmWUYyxq7Bq0PMDOLwGFv7N6/EFosGDYeFC+Ogj9/7Uty9cfLF7XxI5nfLwJ0sCTGKi605v3tz1Qt1xB2zcCPfd5+aFKRcS58Cyf7plPJoUYzoDYPrW6czZMYe7z7qb4GL0aknZd0+ve0g4mlC09fpyqzMU2jwIG9+DzcU8RykTHOzW9Vu3zg0BTpzopmW57jrYtMnf0UmgUjIlJWbfPnjwQVcP9cILcNFF7hPfiy+W8bqovFL3w+wxULGBWy6kKEu/5PLUzKeIjozm+s7XexbPGOs2CSxeaJeBjQbSqXYnXpjzAlk2q3gn6fAvN2XCvJvg0GqP4ilNKlZ0xembNrk7i7/80hWpjx0L20r3EobiA0qmxOf273dvSo0awbPPwqhRbq6X//7XJVblSlYGzLocUnZBn/9BWNVinWbhroVM3DiRu866S9MhSIGMMTzQ5wHW7F3D1yu/Lt5JgkKg9/8gJBJmXgIZR70bZICLioLnn3dJ1c03u7uNmzeH22/XTOpygpIp8Zk9e9y6WI0buyUdzj0Xli+Hzz93MxCXS0segPhJbqbpWj2LfZqnZz5N1fCq3NLtFi8GJ2XR6DajaRPVhsd+f4zMrMzinaRiLPT+DA6vdgXpxe3lKsXq1IH//AfWr3dDfm+9BU2awI03un1SvimZEq/buNGtodewITzzjFv2Zdky103etq2/o/OjzZ/BmhegxW3QtPhDcwt2LeDb1d9yR887qBpRvJ6tk/za1W0SWLzULsFBwTza/1FW713N16uK2TsFrn6q8/Ow/TtY9ojHcZVWDRrA22+7mqobbnCLKLdqBZdd5hZWlvJJyZR4zeLFcPnlbsLNDz6Aa66BNWvg66+hfXt/R+dniXNg3g0QPQC6vOjRqR6a8hA1K9Tknt73eCe2A4vcJoHFi+2Su3cqIyuj+CdqeSc0vQFWPuk+HJRjjRvD66/Dli3u5plff3XL04wYAXFxmqeqvFEyJR7JzIQff3S3FHfp4t5Q7rvPvcG8845LrMq9Q2vg95FQoR6c/RUEhRb7VFM3T2XSpkk83PdhqoRX8WKQUpYFmSCeGPgEa/au4b1F7xX/RMZAt9chuj/MvR4SZngvyFKqdm3XA79tGzz1lJtaYeBAl1h9+KFmVC8vlExJsRw86O7Ia9YMLrzQ1Qw8+6x7Q3nmGVdfILgZzqed4xKoQRMgIqrYp8qyWdw/+X7qV6nPLd1VKyVFc2GrC+nboC+PTHuEw6mHi3+i4DDo+y1Uauw+JBxY4rUYS7Nq1dzdylu3wnvvuaWxrr/eDQs+8gjs3u3vCMWXlExJkaxcCX/9K9St61Zdb9AAvvnG3eny97+72YMlW9oBiBsBafthwHio1MSj0324+EMW7FrAU4OfIiKkvEzIJd5ijOHFc14kMTmRZ2Y+49nJwmvCwIkQWsV9WDisCuwcFSrAX/4CS5fClCluJvUnnnA1pFdeCdOnawiwLFIyJWd09KirgerVC9q1c19ffrmrkfr9dzdDcEiIv6MMMGkHYeowd/dT32+hRhePTncg5QAPTnmQsxuczZXtr/ROjFLudIvtxlUdruLFOS+yfp+HCVBkAxg4yd3ZN20oHN3unSDLCGNg0CD46SdXrH7LLTBuHPTv79b/e/FFN/eelA1KpqRACxe6eVXq1HGftHKG9nbsgPffh06d/B1hgMpJpA4uhb7fQZ1hHp/y0bhH2Zeyj/+M+A+mmJN8igD8e8i/CQ8J55Zxt2A97SKp2goG/uYmop3cH5K2eCXGsqZZM3jlFdi1yy1VU6MG3HMPxMa63qrff1dvVWmnZEpOkpjo7lDp0sUtNPzJJ/CnP8GMGbBqFdx9N9Sq5e8oA1jaQTfscXAJnP0t1B3p8Slnb5/Na/Ne45Zut9CpdiePz3eKpje6TQKLj9qlTuU6PDP4GaZsnsJny71wR16NrjBoshvWntwfjmz0/JxlVMWKbqma2bPddDE33eR6qwYMcLOrP/44bN7s7yilOJRMCcnJ8MUXMHKk+6R0223uU9Lrr7tPUh9/DGefXexVT8qP5F0wuR8cWAxnfw31zvf4lCnpKVz/4/U0qNqApwc/7YUg89HzHbdJYPFhu9zU7SZ61u3JXRPuIuFogucnrNUDBk+FzKPud6AcLTtTXO3bw6uvnuitio11hepNmrgFlt95Bw4c8HeUUlhKpsqpzEyYNMl9SoqJgSuucAWTd9/tHhcvdoXm1ar5O9JS4vBamNQbkja7YvN6F3jltP8X93+s3beWd89/l8rhlb1yTpEgE8T7o97nSOoRbvjpBs+H+wBqdIbB08BmwqQ+mjahkHJ6q+Li3JQyTz4Je/e6XqvatWH0aDf9jKZYCGxKpsqRjAx3d8ktt7i78YYNgx9+cDP3Tpvmbul99lno0MHfkZYyibNh0tmQkQxD4qD2EK+cdsqmKTw3+zlu7HIjQ5sO9co587V/odsksPi4XdpGt+WZIc/w87qfeXfRu945abX2MGwORETD1CGw9UvvnLecaNjQLcG1ahXMn+9qVqdPd9PPREe7+qoffoCUFH9HKnkpmSrj0tLcRJo33OA+5QwZ4uqg+vZ1M5Pv2ePmRBkwAIL0f0OR1U4eD1MGQGhVGDrL1Y94wZ6kPVz1/VW0rNWSl855ySvnLNBv3dwmgaUE2uVvPf/GkCZDuGvCXaxMWOmdk1ZqDENnQ80eblHvFU+Uy7X8PGGMq1l95RW3mPKvv8Kll8Jvv7ka1uhoN5rw3XeuTEP8T38+y6CDB+Grr9xyLtHRboHhr76Cc86Bb791ReZff+26jyM0XVHxZGXAwjtpdfA5Nxv0OfOgSnOvnDozK5Orv7+ag8cO8tXor4gMi/TKeUXyCjJBfHzhx1QOq8xFX13k2WSeuYXXgEGToNGVsOyfMOMigrOOeufc5UxoKAwf7j70xsfDxIkwZgxMnuympYmKcj1X77/vnhf/0OxAZYC1bg28cePgl19g5kxXE1WjhvslGz3a9UgpcfKSo9th9hWQOIvtkaOpP+B/EOS9X6X7J9/PpE2TePf8d2kfU94XNRRfi60cy1eXfMWgjwdx3Q/X8c2l3xBkvPA5OzgCen0KNbrD4nvoGrwIDv4K1crzaueeCQ2FoUPd9vrrbgjw22/h559dXRVAjx5w/vlu69BBNw6VFPVMlVIpKTBhAvztb24OkzZt3Jp4+/e7mchnzoSEBHeXyMiRSqS8ZsdP8GtHOLAUen/Gxqq3ejWR+mjJR7ww5wVu634bN3S5wWvnFTmdfg378dzQ5/h+zfc8POVh753YGGh1BwyaQkhWEkzoBuve0KRKXhAS4iYFff11V++6dKmbad0Yd1dgp06uBuvGG91IxP79/o64bFPPVCmRmQnz5rmu3cmT3TwlqakuSRo82CVS557rlncRH0g/Aov/DhvegupdoM8XblhvS5zXLjFhwwTG/jyWwY0H89JwH9dJieRx51l3snbfWp6Z9QyNqzdmbNex3jt5TH/mR71Hn6D3YMGtsOtXOOt9V6guHjPG9UJ16AAPP+xqYXNGKr7+2g0R5tRhDR3qbj7q1cvfUZctSqYClLWwdq27+27yZJg06WyOZpccdOzo5oIaPNgtTVCxon9jLfPiJ8Mff4Hk7dDqHuj4JASHe/USf+z4g4u+uog2UW345tJvCPFib5dIYRhjeO3c19h+eDu3jLuFGhVqMLrNaK+dPz24BvQfB+v+4z6YjGsDXV6CRldpLMrLYmLcIsvXX+/u4p4/302FM3Giu2P7qacgMhLat2/P6NHu70inTloWzBP6pwsQGRmum3bmTDfb+MyZ7tMFQKNGMGBAAldfHcvAga6oXEpASjwseQA2fwyVW8DQmRDV2+uXWbBrAed+di6xlWOZcNUEqkVU8/o1RAojJCiEL0d/yfD/DueKb68gNCiUC1p5Z840wCVNLf/mpg+ZewPMuQa2fAbd33R3AYrXhYS4Xqhevdzw36FDbk6rSZPgp58qcO+97rhKlaBPH5dY9evnerHCvfuZsUxTMuUnR4+6Tws5idPs2ZCU5J5r1Mh1w/bt63qfmjSBuLh1DBgQ69eYy42sdFj3Giz/P8hMgTb3Q7tHIaSC1y81e/tsRnw2gpoVajLp6knEVIrx+jXOaPiCkr+mnJmf2qVSWCXGXzmeYZ8O45KvL+Gziz7jkraXePciVdvAkBmw/g1Y+iD80hpa3wNtHoBQTU7rS1WrwgUXuG306Hm0bDmA6dM5vj30kDsuIsIlYH36wFlnQc+eWkrsdJRMlYCMDDcJ27x5J7YVK1wdlDFuWYFrrnHJ09lnQ716/o64nLIWdv8Gi++FQ6ugzgjo+jJUaeGTy41bN47LvrmM2MqxTL12KvWq+KnhvTQ3lniZH9ulSngVfrvqN0Z+PpLLvrmMfSn7uLnbzd69SFAwtLwd6v8JljwIK5+CjR9Ax6egybXgjTsK5Yzq1HETN192mft+7173AX/6dLcA89NPu79VAE2buqTqrLPc1rEjhIX5L/ZAomTKy7Ky3JIACxacSJwWLjwxsVr16u7W1VGj3P+UvXu7feJne6bB0n/A3tlQqQn0+8ktUuyjWo435r/B7b/eTqfanRg3Zhy1K9X2yXVEiqtaRDUmXj2RS7++lFvG3cK6fev499B/e7+er2I96P0ptLgNFt4Jc6+HtS9Du0dcoqWkqkTVquWm1LnwQvf90aPub9jcufDHH26I8PPP3XPh4dClC3TvDp07u69bt3ZTOJQ3SqY8cOwYrFwJS5a4belStx3OnvcuPNz9D3bjjS6B6tHDZfaqtQwQ1kLCdFjxL9gzFSrUhe5vQZM/Q7BvPm4lpydz6/hb+WjJR5zX/Dy+GP0FlcIq+eRahTY3+64tLXYcWAKgXSqGVuT7y77nnon38NIfL7F0z1K+HP0ltSr6YLynVk8YNtstQbP8UZg5Gqq2g/aPQP2LlVT5SWSkq6Hq1+/Evh07TiRXf/zh7hbM6TAID4d27U4kV507u7sMy/qNUkqmCiErC7Ztc0N1K1fCsmUueVq9+kT3Z6VK7n+Yq65yd0Xk/A+kLtAAlJUO276BNS+4tc8iYqDrK9BsrJto0EdWJ67mkq8vYVXiKv7Z75882v9RgoOCfXa9QtuYvS6bkqnAEiDtEhocyqsjXqVrna7c9MtNdHunG59d9Bl9GvTx/sWMgUaXQ4NLYOsXsPJxmHkpVGnlCtcbXwMhWhHA3+rVc9vFF7vvMzNh/XpYvBgWLXKP333nkixwS5W1aOGSrLZt3daunZsjsaz0YimZyiUz0w3R5SRNq1a5bfXqk9c/qlvXJUwXXOAeO3VyReJa2y7ApcTDpo9c0WvydqjSEnq8DY2u9klxeY7MrExem/caD019iMjQSH676jeGNR3ms+uJ+MK1na6lbXRbLv36Uvp+2Jd7et3D44MeJyLEBx9AgoKh8ZXQ8HLY9pX74DP/r7DkIWj6F2hxq+7+CyDBwdCqlduuuMLts9Z1Qixe7LalS10nxLffnpizNTQUWrY8OcFq2xYaNy59SVa5S6asdesXbdjgMumcx/Xr3bxOx46dOLZePTez+Nix7rFNGzceXKOG/+KXIsrKcEXlG9+Dnb+AzYSYge5W7NgRPh86WL5nOTf8fAPzds5jRLMRvHv+u9StUten1xTxlW6x3Vh2yzLum3gfz895nnHrx/HmeW/Sv1F/31wwKBgaXeGSqr1zYO0rrp5qzQsQM8gNyde/CELK+BhSKWSMm4G9YcMT9VfgOibWrHEdFitWuMe5c+HLL08cExLiEqoWLU7emjd3nRmB2HFRZpOpQ4dcJpw3adqwgeOTX4JrtCZNXHfjkCEnJ01Vq/ovfvFAViYkzoBtX8P2b+HYHjeU1/peaHK9z+7Oy21P0h4en/44by98m+oR1fn8os+5vN3lGBXMSSlXKawSb458k4taX8SNP9/IgI8HcFHri3hu6HM0qd7ENxc1xs3xFtXbrY256SPY/BHMudr1WDW4BBqMhpjBPqt3FO+oWNHVUnXpcvL+pKQTo0Hr18O6dW6bOtUtn5ajQgWXVDVv7v5uN23q/oa3b+/fORjLbDI1aRJckj01Sk7C1Lw5DBhwohGaN3fLr2jW1zIgMw0SZ7rkKSeBCq4AsedBozHuzrwg3/cbHzx2kFf+eIXn5zxPSnoKN3a5kScGPUHNijV9fm2RkjS06VBW37qaF+e8yNMzn+aXdb8wtstY7utzHw2q+nBdq8j60P6f0O5h9zu/6UP3wWnTBxBa1f2u178Y6pyjHqtSpFKlEzdq5ZaVBTt3usQqd5K1bBn89BOkp7vjnnoKHnyw5OPOUWbTiP793ULAzZopYSqzkra4Ibzdv0H8FMhIOpFANbwUYs8tsWLVbYe28fIfL/PuondJSktidJvRPDnoSVrU9H0vmIi/VAitwMP9HubPnf/Mo9Me5e2Fb/P2wre5puM13N3rbtpEtfHdxU0QRPdzW/e33LJP27+FHT+6WdWDIyC6P9QeBnWGujsD1TNc6gQFQf36bhs8+OTnMjPdnYWbNrnhRH8qsylGVJSbRVzKCGshaZMbvkuc6aY0OLLePRfZyK3vFTvC1VGElsxUAxlZGczZN4dXv3yVn9f9jLWWy9pdxn2976NT7U4lEoNXVO9y5mOk5JWidomtHMu7o97ln/3/yXOznuPdRe/y/uL36d+wP7d0u4ULW13o2wCCw6HueW7LSnfvDzt+hPhJsPgeWAxUqAMxQyD6bKjVB6q21nQLpVxw8Im6LH8rs8mUlHKp+2D/IjiwCPYtgL2zIGW3ey6sunszbH4rxA536+aV0CfOzKxMZm+fzXerv+OrVV+x68guoipGcWfPO7mtx200rBYAv9VFNWKhvyOQ/JTCdmlQtQH/Ofc/PNL/ET5Y/AFvL3yby7+9nKrhVTmr2lkk101mSJMhhPmyrikoFGoPdhu4Gqv4yRA/EeInwJZP3f7QalCrl6vDqtEVqndyCZdIMSiZEv/KTIOkDXBotVvC5cBiN/dT8rYTx0Q2guiB7hNlVF+3rlcJfqLcn7Kf37f8zm8bfuOHtT+QcDSBsOAwzml6DjfVv4kHLnrAt38cREqZqMgo7j/7fu7rcx+TNk7ii5Vf8PXyr5nw+QSqR1RnRPMRDGsyjCFNhvj+7tbI+tD0z26zFpI2QuIst+2dDct+PXFsRIxLqqp3guqd3XtN5eY+nX9OygYlU+J7WelwdBsc3QJJm91w3eHVbjuyEWzGiWMrt3CfFKvfBjW6uDe08JKbi8Jay9ZDW1m4ayGzt89m2pZpLIlfgsVSKawS5zU/jz+1+hPnNj+XyuGViYuLUyIlUoAgE8Q5zc7hnGbncEXlK0irl8bXq77mtw2/8flytyZJm6g2DGg4gJ71enJWvbNoXqO57+56NQYqN3Nbk2vdvrRDcHAp7F8MB5e4x/gXcr0vGYhs6CYOrdLSPVZq4j7kRTZQoiWAkinxVGaqG35L2Q3HdkPyruzHnXB0sysST9kBNuvEa0yI+7RXpY2766ZKa1e/ULllidU7ARxJPcK6fetYt28dyxOWs2DXAhbtXsS+lH0AhAWH0bt+bx4b8BgDGw+kR90eZTNx+jz7D9cY69845GRlrF3CgsIY1mIYI1uMJMtmsXzPciZtmsTEjRP5ZNknvLHgDQBqVKhBlzpdaBvV1m3R7rFqhI/mqgmreqKQPUdmqvuwd2gNHF4DR9a6x4TpkJl88usjamcnVg2hUiOoUA8q1HZDhhG13deatb3MK1QyZYwZDrwCBAPvWWufyfN8OPAJ0BXYB1xmrd3i3VDF5zJTIe0ApO13NUt5H0/6OhFSdrnj8zLB7k2kUmP3BlWpMUQ2zn5s5BY29fZiqfk4knqE7Ye3s+PwDrYfyn48vJ2NBzaybt86dh3ZdfzYkKAQ2kW348JWF9K1Tle6xnalQ0wH38zuLFLOBZkgOtbuSMfaHbm3971kZmWyeu9q/tjxB3N3zGXJniW8u+hdktNPJC61K9WmcbXGNKzWkEZVG9GomtvqV61PTGQM1StUJ8hbw//B4SeG+3KzWSd/UDy61fW4H90K+xfAju9cT3xeIZVOJFcR0RBWA8JrZj/WOPn7sBquLjQ4QncfliJn/ItmjAkGXgeGAjuA+caYn6y1q3Id9hfggLW2mTHmcuBZ4DJfBFwuWYuxmZCeBJkpkHks1+OxfPalQNYxyEhxX2ckQfoR95hxxH2dfuTE1xnZz+X3JpDDhOT65a/pepai+7s3iAp1IKLOia/Do9zMxR7KyMogKS2JI6lHOJJ25KTHpLQkjqQdYX/KfvYm7z1p25eyj73Je0lKSzr5R8AQUymGRtUaMbTJUFrWbEnLWi1pUbMFzWs0Jzwk3OOYRaTogoOCaRfdjnbR7bihyw0AZNksth7cysrElaxIWMH6fevZcmgL83bO45tV35CRlXHSOUKCQoiqGEV0ZPTxLapiFFUjqlI1vCpVI6pSJbzK8a+rhrvvK4ZWpEJoBUKDQs88vGiCXA1WZP2Te7Jy2CxI3euWrkrZDcfi3Zay2+07ttvVhqbtd9tp33ODIaSy660PqQyhlfN5rOQegytkbxF5Hk+zLyjsxLou4rHCdA/0ADZYazcBGGO+AC4AcidTFwD/l/31N8Brxhhjrf9aKjFxEcvXfQ7WYm0WkIXNygQs2KzsfTZ7v/v6+D6bhSXL/Y92/NjsR2tzHeu+zzn2pNfbTLd0ic1w17WZWJuRvS8Tm5WRvS/TLXmS83XOa2wWZGVgyXQzegNfrTvx89k8j6d8bXPtM0EQHIE9/ksUgc3+xbLB1dy+sJx9FbEhkWQFVyQzuILbgiLINCFk2iwybSaZWZnuMTmTjKR0Mu1mMrM2nPxcnseMrAxSM1M5lnGM1IxUUjNTjz8WtO9YRq61fU6jclhlalWsRa2KtYiOjKZNVBtqVqhJbOVY6lWpR70q9ahftT6xlWPL5jCdSBkUZIJoXL0xjas3ZmSLkSc9l5mVye6k3Ww5uIXth7aTcDThxJacwJ6kPWzYv4HE5MRTPlSd7noVQipQIbRCvo9hwWGEBIUQGhxKaFDoqV/nty84lGATTJCpQ5CpS1DFIEykIcgEEYQhyGYQlJmCyUwmKDOFoOxHk5FMUFYqQVnH3GPKMUxSCkFZB92+zBRMZgom89jx2q7caWDelLCg5wzwy4YgCArGmJDsEYNgCArJ/j4YCMEEhbgP1EHB7muynzPBGBOcfUOQyf7aAEEYE+T2m+ATX5P7Ofe6k57Leb0JcnGQ8zXZ5821mZMfm9YfSsOGwwvV1r5QmGSqLrA91/c7gJ4FHWOtzTDGHAJqAntzH2SMGQuMBYiJiSEuLq54URfC0l3vcOf6//ns/KVLFpCcvXlfEEHuzcEEEURQ9pvHyd8Hm2BCg9ybTFhQGKHmxNfVTDXCgsMIDQ09cYwJo0JwBSoEV6BiSEUqBld0Xwfn+jqkIpVCKhEWVECClA7sg8x9mWzJ/s/bkpKSfPr/cUkYkP1Y2n+OHGWhTUDtUlh1sv8jGKiSveWSaTNJyUwhKSOJoxlH3ZZ54jE1M5W0rDRSs1KPb2mZ7vu0jDRS01LZl7WP9Kx098HQZrgPitlfZ2Tl+T7X86VDdscAp+klKwX+HjuTEc39V5ZRogXo1tp3gHcAunXrZgcMGOCza7U73ITOuy46nuUagrKz4OBT9mEMBrffjWqa7K9P5PAmO5/Pb1/u/fntO9PrC3POefPn0aN7jxKLKcgEERzkkqCCHkOCQggyQeV6vbm4uDh8+f9xiXA3VZX+nyNbmWgTULuUctba44mWtZYsm3V8s5z8fZbNOuWY/I7Le8zxa+Ual8g7IFTQcxbLwoUL6dq1a5Fek/dn9NZryBn5sZm4UZ/sDXt8ROj4Zk99bBzVhvo1fTjj/hkUJpnaCdTP9X297H35HbPDGBMCVMUVovtNrSoN6FfFh+tDlbDEyETaRrf1dxgiIlIIxhg35Ifv1wQtrqR1SXSL7ebvMMqEwiRT84HmxpjGuKTpcmBMnmN+Aq4F5gCjgan+rJcSkSLo8ba/I5D8qF1ESo0zJlPZNVC3ARNwo9IfWGtXGmP+BSyw1v4EvA98aozZAOzHJVwiUho0G+vvCCQ/aheRUqNQNVPW2vHA+Dz7Hsn19THgEu+GJiIiIhL4tGS2SHm34R23SWBRu4iUGlpORqS8m3eTe9SwUmBRu4iUGuqZEhEREfGAkikRERERDyiZEhEREfGAkikRERERDyiZEhEREfGAkikRERERD2hqBJHyboxWfgpIaheRUkM9UyIiIiIeUDIlIiIi4gElUyIiIiIeUDIlIiIi4gElUyIiIiIeUDIlIiIi4gElUyIiIiIeUDIlIiIi4gElUyIiIiIeUDIlIiIi4gElUyIiIiIeUDIlIiIi4gElUyIiIiIeUDIlIiIi4gFjrfXPhY1JBLb65eKlUy1gr7+DkFOoXQKP2iQwqV0Cj9qkaBpaa6Pye8JvyZQUjTFmgbW2m7/jkJOpXQKP2iQwqV0Cj9rEezTMJyIiIuIBJVMiIiIiHlAyVXq84+8AJF9ql8CjNglMapfAozbxEtVMiYiIiHhAPVMiIiIiHlAyVQoZY+4xxlhjTC1/x1LeGWOeM8asMcYsM8Z8b4yp5u+YyjNjzHBjzFpjzAZjzAP+jqe8M8bUN8ZMM8asMsasNMbc4e+YxDHGBBtjFhtjfvF3LGWBkqlSxhhTHxgGbPN3LALAJKCdtbYDsA540M/xlFvGmGDgdWAE0Aa4whjTxr9RlXsZwD3W2jbAWcCtapOAcQew2t9BlBVKpkqfl4C/Ayp2CwDW2onW2ozsb/8A6vkznnKuB7DBWrvJWpsGfAFc4OeYyjVr7W5r7aLsr4/g/njX9W9UYoypB5wHvOfvWMoKJVOliDHmAmCntXapv2ORfF0P/OrvIMqxusD2XN/vQH+4A4YxphHQGZjr51AEXsZ9KM/ycxxlRoi/A5CTGWMmA7Xzeeph4CHcEJ+UoNO1ibX2x+xjHsYNaXxWkrGJlAbGmErAt8Cd1trD/o6nPDPGjAQSrLULjTED/BxOmaFkKsBYa4fkt98Y0x5oDCw1xoAbTlpkjOlhrY0vwRDLnYLaJIcx5jpgJDDYaq4Rf9oJ1M/1fb3sfeJHxphQXCL1mbX2O3/HI/QBRhljzgUigCrGmP9aa6/yc1ylmuaZKqWMMVuAbtZaLVLpR8aY4cCLQH9rbaK/4ynPjDEhuJsABuOSqPnAGGvtSr8GVo4Z98nvY2C/tfZOP4cjeWT3TN1rrR3p51BKPdVMiXjmNaAyMMkYs8QY85a/Ayqvsm8EuA2YgCt0/kqJlN/1Aa4GBmX/fizJ7hERKVPUMyUiIiLiAfVMiYiIiHhAyZSIiIiIB5RMiYiIiHhAyZSIiIiIB5RMiYiIiHhAyZSIiIiIB5RMiYiIiHhAyZSIiIiIB/4f19CFiNg0gqkAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10,6))\n", "\n", "plt.title('Finite Square Well', fontsize=15)\n", "\n", "colors = ['blue','orange','green']\n", "\n", "for clr, elmt in zip(colors, eqns):\n", " expx, cosx = elmt\n", " \n", " xseg1 = np.linspace(-5,-1, N)\n", " f1 = lambdify(x, expx)\n", " yval = f1(-xseg1)\n", " plt.plot(xseg1, yval, color=clr)\n", " \n", " xseg2 = np.linspace(1,5, N)\n", " yval = f1(xseg2)\n", " plt.plot(xseg2, yval, color=clr)\n", " \n", " f2 = lambdify(x, cosx)\n", " xseg3 = np.linspace(-1,1, N)\n", " yval = f2(xseg3)\n", " plt.plot(xseg3, yval, color=clr)\n", " \n", "ymin, ymax = plt.gca().get_ylim()\n", "xvlines = [-1, 1]\n", "plt.vlines(xvlines, ymin, ymax, linestyle='dashed', color='orange', lw=2)\n", " \n", "plt.grid() " ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/latex": [ "$ \\left \\{ \\begin{matrix} E = V_{0} - \\frac{0.226846595732537 \\hbar^{2}}{m} & E = V_{0} + \\frac{0.273108886577841 \\hbar^{2}}{m} \\\\ E = V_{0} - \\frac{1.46988327214104 \\hbar^{2}}{m} & E = V_{0} + \\frac{0.530333730361958 \\hbar^{2}}{m} \\\\ E = V_{0} - \\frac{3.81657632689217 \\hbar^{2}}{m} & E = V_{0} + \\frac{0.684640722250683 \\hbar^{2}}{m} \\end{matrix} \\right \\} $" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The code under here is doubtful given the way it tries to calculate the energies and ends up\n", "# with contradictory answers.\n", "s = \"\"\n", "for elmt in eqns:\n", " expx, cosx = elmt\n", " expxdiff = expx.diff(x,x)\n", " cosxdiff = cosx.diff(x,x)\n", " expr_exp = sym.solveset(sym.simplify((expx.diff(x,x)+2*m/hbar**2*(E-V0)*expx)/expx), E)\n", " cosx_exp = sym.solveset(sym.simplify((cosx.diff(x,x)+2*m/hbar**2*(E-V0)*cosx)/cosx), E)\n", " #display(Eq(E,expr_exp.args[0]), Eq(E, cosx_exp.args[0]))\n", " e1latex = (sym.latex(Eq(E,expr_exp.args[0])))\n", " e2latex = (sym.latex(Eq(E,cosx_exp.args[0])))\n", " s += \"{} & {} \".format(e1latex, e2latex) \n", " \n", " # use this to detect if at last index of for loop\n", " if elmt is not eqns[-1]:\n", " s += r\" \\\\ \"\n", " #display_latex (\"$ \"+e1latex+\" $\", raw=True)\n", "\n", " #display_latex('E = V_{0} - \\\\frac{0.226846595732537 \\\\hbar^{2}}{m}', raw=True)\n", "s = r\"$ \\left \\{ \\begin{matrix} \" + s + r\"\\end{matrix} \\right \\} $\"\n", "\n", "display_latex(s, raw=True)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }