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Created April 16, 2020 22:29
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Cálculo de función radial de hidrógeno.
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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy.special import factorial,genlaguerre\n",
"import pylab as pl"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Funciones radiales de hidrógeno:\n",
"$$\n",
"R_{n,l}(\\rho) = \\sqrt{\\left(\\frac{2}{n}\\right)^3\\frac{(n-l-1)!}{2n(n+l)!}}e^{-\\rho/n}\\left(\\frac{2\\rho}{n}\\right)^l L_{n-l-1}^{2l+1}\\left(2\\rho/n\\right)\n",
"$$\n",
"con $\\rho=r/a_0$."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9999928039327279"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"n = 15\n",
"l = 0\n",
"\n",
"ρ = np.linspace(0,800,1000)\n",
"Rnl = np.sqrt((2/n)**3 * factorial(n-l-1)/(2*n*factorial(n+l)))*np.exp(-ρ/n)*(2*ρ/n)**l * genlaguerre(n-l-1,2*l+1)(2*ρ/n)\n",
"\n",
"# Graficar\n",
"pl.figure(dpi=150)\n",
"pl.plot(ρ, Rnl**2*ρ**2)\n",
"pl.xlabel(r\"$\\rho$\")\n",
"pl.ylabel(r\"$|R_{n,l}(\\rho)|^2\\rho^2$\")\n",
"\n",
"#Verificar normalización\n",
"np.sum(np.abs(Rnl)**2*ρ**2*(ρ[1]-ρ[0]))"
]
},
{
"cell_type": "code",
"execution_count": null,
"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": "3.8.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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