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@asafpm
Created April 10, 2021 01:13
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Solución a la ecuación de Shrödinger para el pozo cuadrado usando el método de Numerov
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{
"cells": [
{
"cell_type": "markdown",
"id": "eefa86b2-3995-43a9-9686-e759dfeb5613",
"metadata": {},
"source": [
"# Numerov\n",
"Usando el Método de Numerov"
]
},
{
"cell_type": "markdown",
"id": "162524fb-b202-4466-8844-4f670e802b10",
"metadata": {},
"source": [
"## Para un potencial cuadrado\n",
"<img 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\" />"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "da11468e-64c6-4203-9588-4e8da0cb44c2",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pylab as pl\n",
"from scipy.optimize import root, bisect"
]
},
{
"cell_type": "markdown",
"id": "existing-voltage",
"metadata": {},
"source": [
"Definimos los parámetros del problema"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "inclusive-juvenile",
"metadata": {},
"outputs": [],
"source": [
"a=2\n",
"V0=1.5\n",
"\n",
"h = 1e-4\n",
"xm = 4\n",
"\n",
"x = np.arange(-xm,xm+h,h)\n",
"n = len(x)\n",
"\n",
"V = -V0*((-a <= x) & (x <= a))"
]
},
{
"cell_type": "markdown",
"id": "wireless-malawi",
"metadata": {},
"source": [
"Graficamos el potencial"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "6e33cd8b-1461-464f-8a06-6b550122fa56",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fd49ec3fbe0>]"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pl.plot(x,V)"
]
},
{
"cell_type": "markdown",
"id": "neural-waters",
"metadata": {},
"source": [
"Solución para varias energías de prueba"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "7582a3be-086d-4a2d-922c-7903da101401",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pl.figure(dpi=120)\n",
"\n",
"for E in [ -V0+0.07, -V0+0.1, -V0+0.2, -V0+0.3]:\n",
" \n",
" y = np.zeros(n)\n",
" Q = 2*E-2*V\n",
"\n",
" y[0] = 0\n",
" y[1] = 1e-6\n",
"\n",
" for i in range(1,n-1):\n",
" y[i+1] = ( 2*(1-5*h**2*Q[i]/12)*y[i]-(1+h**2*Q[i-1]/12)*y[i-1] )/(1+h**2*Q[i+1]/12)\n",
" \n",
" pl.plot(x,y)\n",
" \n",
"pl.ylim(-0.4,0.7)\n",
"pl.xlim(-3,3)\n",
"pl.xlabel(\"$x$\")\n",
"pl.ylabel(r\"$\\psi(x)$\")\n",
"pl.axvline(-a, ls='--', color='gray')\n",
"pl.axvline(+a, ls='--', color='gray')\n",
"pl.annotate(\"integración\", xy=(1, -0.2), xytext=(-1, -0.2), arrowprops=dict(arrowstyle=\"->\"))\n",
"pl.savefig(\"potencial_cuadrado_chafa.png\")"
]
},
{
"cell_type": "markdown",
"id": "convenient-luther",
"metadata": {},
"source": [
"Ahora integramos de izquierda a derecha y de derecha a izquierda y calculamos el error de la unión. "
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "ccead034-8ed7-4353-9f59-80193d622672",
"metadata": {},
"outputs": [],
"source": [
"nc = int(n/2) # índice de punto de pegado\n",
"\n",
"def err(E):\n",
" Q = 2*E-2*V\n",
" \n",
" y = np.zeros(n)\n",
" y[0] = 0\n",
" y[1] = 1e-6\n",
" # Integramos de izquierda a derecha\n",
" for i in range(1,nc+1):\n",
" y[i+1] = ( 2*(1-5*h**2*Q[i]/12)*y[i]-(1+h**2*Q[i-1]/12)*y[i-1] )/(1+h**2*Q[i+1]/12)\n",
" \n",
" γf = (y[nc+1]-y[nc-1])/(2*h*y[nc]) # psi'/psi\n",
"\n",
" y = np.zeros(n)\n",
" y[n-1] = 0\n",
" y[n-2] = 1e-6\n",
" # Integramos de derecha a izquierda\n",
" for i in range(n-2,nc-1,-1):\n",
" y[i-1] = ( 2*(1-5*h**2*Q[i]/12)*y[i]-(1+h**2*Q[i+1]/12)*y[i+1] )/(1+h**2*Q[i-1]/12)\n",
" \n",
" γb = (y[nc+1]-y[nc-1])/(2*h*y[nc]) # psi'/psi\n",
" \n",
" return (γf-γb)"
]
},
{
"cell_type": "markdown",
"id": "interested-beverage",
"metadata": {},
"source": [
"Con un método para encontrar raíces encontramos la energía que haga el error de unión cero."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "24c4a93d-42c0-4dca-bc01-97580d63d9a6",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"-1.3158358960339682"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"E0 = bisect(err,-1.4,-1)\n",
"E0"
]
},
{
"cell_type": "markdown",
"id": "tender-genesis",
"metadata": {},
"source": [
"Calculamos la solución con el eigenvalor encontrado y la graficamos. Para este caso sencillo es suficiente calcular la solución de izquierda a derecha ya que encontramos el eigenvalor pero si aumentamos el dominio o cambiamos el potencial puede que no continúe siendo así y sea necesario calcular la solución con integración en distintas direcciones como hicimos para encontrar el eigenvalor."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "372036be-cd0d-4d4b-bb99-54a56beabd07",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pl.figure(dpi=120)\n",
"\n",
"for E in [E0]:\n",
" Q = 2*E-2*V\n",
"\n",
" y[0] = 0\n",
" y[1] = 1e-6\n",
"\n",
" for i in range(1,n-1):\n",
" y[i+1] = ( 2*(1-5*h**2*Q[i]/12)*y[i]-(1+h**2*Q[i-1]/12)*y[i-1] )/(1+h**2*Q[i+1]/12)\n",
" \n",
" # Normalizar\n",
" norm = np.sum(y**2)*h\n",
" y = y/np.sqrt(norm)\n",
" \n",
" pl.plot(x,y)\n",
" \n",
"pl.xlabel(\"$x$\")\n",
"pl.ylabel(r\"$\\psi(x)$\")\n",
"pl.axvline(-a, ls='--', color='gray')\n",
"pl.axvline(+a, ls='--', color='gray')\n",
"pl.savefig(\"potencial_cuadrado_bien.png\")"
]
},
{
"cell_type": "markdown",
"id": "ba34a02a-c7ee-4179-9f06-98776b2eecb5",
"metadata": {},
"source": [
"# Encontrar todas las raíces #"
]
},
{
"cell_type": "markdown",
"id": "artistic-drinking",
"metadata": {},
"source": [
"Parámetros del problema"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "56b1f96a-c715-42fe-b81a-900cd829b9cf",
"metadata": {},
"outputs": [],
"source": [
"a=2\n",
"V0=3.5\n",
"\n",
"h = 1e-4\n",
"xm = 4\n",
"\n",
"x = np.arange(-xm,xm+h,h)\n",
"n = len(x)\n",
"y = np.zeros(n)\n",
"\n",
"V = -V0*((-a <= x) & (x <= a))"
]
},
{
"cell_type": "markdown",
"id": "conventional-lover",
"metadata": {},
"source": [
"Definición de función de error y punto de encuentro"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "multiple-labor",
"metadata": {},
"outputs": [],
"source": [
"nc = int(n/2) # índice de punto de pegado\n",
"\n",
"def err(E):\n",
" Q = 2*E-2*V\n",
" \n",
" y = np.zeros(n)\n",
" y[0] = 0\n",
" y[1] = 1e-6\n",
" # Integramos de izquierda a derecha\n",
" for i in range(1,nc+1):\n",
" y[i+1] = ( 2*(1-5*h**2*Q[i]/12)*y[i]-(1+h**2*Q[i-1]/12)*y[i-1] )/(1+h**2*Q[i+1]/12)\n",
" \n",
" γf = (y[nc+1]-y[nc-1])/(2*h*y[nc]) # psi'/psi\n",
"\n",
" y = np.zeros(n)\n",
" y[n-1] = 0\n",
" y[n-2] = 1e-6\n",
" # Integramos de derecha a izquierda\n",
" for i in range(n-2,nc-1,-1):\n",
" y[i-1] = ( 2*(1-5*h**2*Q[i]/12)*y[i]-(1+h**2*Q[i+1]/12)*y[i+1] )/(1+h**2*Q[i-1]/12)\n",
" \n",
" γb = (y[nc+1]-y[nc-1])/(2*h*y[nc]) # psi'/psi\n",
" \n",
" return (γf-γb)"
]
},
{
"cell_type": "markdown",
"id": "prospective-theorem",
"metadata": {},
"source": [
"Buscamos intervalos donde la función de error cambia de signo para buscar la raíz en ese intervalo"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "6d760b30-9542-46c0-9c70-60da3161ba4f",
"metadata": {},
"outputs": [],
"source": [
"ΔE = 0.5\n",
"Et = -V0\n",
"yp = err(Et)\n",
"\n",
"E0s = []\n",
"\n",
"while Et < 0:\n",
" yt = err(Et+ΔE)\n",
" if yt*yp < 0 :\n",
" E0 = bisect(err, Et, Et+ΔE )\n",
" E0s.append(E0)\n",
" Et += ΔE\n",
" yp = yt"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "recorded-stroke",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-3.282560353711233, -2.639927386871932, -1.6105597788755404, -0.3198443212040729]\n"
]
}
],
"source": [
"print(E0s)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "f37b0b77-38cf-4f54-b554-ec5da3fc882f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pl.figure(dpi=120)\n",
"\n",
"for E in E0s:\n",
" Q = 2*E-2*V\n",
"\n",
" y[0] = 0\n",
" y[1] = 1e-6\n",
"\n",
" for i in range(1,n-1):\n",
" y[i+1] = ( 2*(1-5*h**2*Q[i]/12)*y[i]-(1+h**2*Q[i-1]/12)*y[i-1] )/(1+h**2*Q[i+1]/12)\n",
" \n",
" # Normalizar\n",
" norm = np.sum(y**2)*h\n",
" y = y/np.sqrt(norm)\n",
" \n",
" pl.plot(x,y+E)\n",
" pl.axhline(E, lw=0.5, color='gray')\n",
" \n",
"pl.xlabel(\"$x$\")\n",
"pl.ylabel(r\"$\\psi(x)$\")\n",
"pl.axvline(-a, ls='--', color='gray')\n",
"pl.axvline(+a, ls='--', color='gray')\n",
"pl.savefig(\"potencial_cuadrado_niveles.png\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "strategic-church",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.9.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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