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@tkmharris
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Functions for creating images of hydrogen orbitals
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Hydrogen orbitals\n",
"\n",
"The normalisition wavefunctions $\\psi_{n\\ell m}$ for the single electron in a hydrogen atom are given in spherical coordinates $(r, \\theta, \\phi)$ by\n",
"\n",
"$\\psi_{nlm}(r, \\theta, \\phi) = \\sqrt{\\left(\\frac{2}{na_0^\\ast}\\right)^3 \\frac{(n-l-1)!}{2n(n+l)!}} e^{-\\rho / 2} \\rho^l L_{n-l-1}^{2l+1}(\\rho) Y_{l}^{m}(\\theta, \\phi),$\n",
"\n",
"where:\n",
"* $\\rho = \\frac{2r}{na_0^\\ast}$;\n",
"* $a_0^\\ast = \\frac{4\\pi\\epsilon_0\\hbar^2}{\\mu e^2} \\approx 5.2946541\\times10^{-11}$;\n",
"* $L_{n-l-1}^{2l+1}(\\rho)$ is a generalized Laguerre polynomial of degree $n-l-1$;\n",
"* $Y_l^m(\\theta, \\phi)$ is a spherical harmonic function, degree $l$, order $n$;\n",
"* the quantum numbers $n,l,m$ can be:\n",
" - $n = 1,2,3,\\dots$\n",
" - $l = 0,1,\\dots, n - 1$\n",
" - $m = -l, \\dots, l$.\n",
" \n",
"We want to plot these basis solutions for various $n,\\ell,m$. We will be plotting projections to the $xy$-plane."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Scipy are built in special functions for spherical harmonics and generalized Laguerre polynomials. \n",
"* $Y_{\\ell}^{m}(\\theta, \\phi)$ is given by `scipy.special.sph_harm(m, l, theta, phi)`\n",
"* $L_{n-\\ell-1}^{2\\ell + 1}(\\rho)$ is given by `scipy.special.genlaguerre(n - l - 1, 2*l + 1)`"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"from scipy.special import sph_harm, genlaguerre"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that $\\psi_{nlm}(r, \\theta, \\phi)$ can be split into a product of the spherical harmonic $Y_{l}^{m}(\\theta, \\phi)$, which is independent of $r$ (and of $n$), and a function of $r, n, l$:\n",
"\n",
"$\\sqrt{\\left(\\frac{2}{na_0^\\ast}\\right)^3 \\frac{(n-l-1)!}{2n(n+l)!}} e^{-\\rho / 2} \\rho^l L_{n - l -1}^{2l + 1}(\\rho)$.\n",
"Let us call this function $\\Psi_{nl}(r)$."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"A0_STAR = 5.2946541e-11 # The (reduced) Bohr radius A0_STAR is a constant of the universe\n",
"\n",
"def big_psi(qnum_n, qnum_l, radius):\n",
" \"\"\"\n",
" The radial component of the elctron probability denisty.\n",
"\n",
" qnum_n: integer, 0 <= qnum_n\n",
" qnum_l: integer, 0 <= qnum_l <= qnum_n-1\n",
" radius: real, 0 < raius\n",
"\n",
" big_psi(qnum_n, qnum_l, radius): real\n",
" \"\"\"\n",
"\n",
" rho = (2*radius) / (qnum_n*A0_STAR)\n",
" L = genlaguerre(qnum_n - qnum_l - 1, 2*qnum_l + 1)(rho)\n",
"\n",
" factorial = lambda x: np.prod(np.arange(1, qnum_n + 1)) # good enough factorial for small numbers\n",
" sqrt_term = np.sqrt(((2/qnum_n*A0_STAR)**3) * factorial(qnum_n - qnum_l - 1) / (2*qnum_n*factorial(qnum_n + qnum_l)))\n",
"\n",
" result = sqrt_term * np.exp(-rho/2) * (rho**qnum_l) * L\n",
"\n",
" return result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now use `big_psi` and the sphericcal harmonic `sph_harm` to define $\\psi_{nlm}$. \n",
"The spherical harmonics, and thus $\\psi_{nlm}$, are complex-valued in general. Since we want to plot probabilities, not amplitudes, we are only interested in the norm square $|\\psi_{nlm}|^2$.\n",
"So we define a function `psi_normsq` for this."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def psi_normsq(qnum_n, qnum_l, qnum_m, radius, theta, phi):\n",
" \"\"\"\n",
" Multiply the radial component big_psi by the appropriate spherical harmonic and take the norm-square.\n",
"\n",
" qnum_n: integer, 0 <= qnum_n\n",
" qnum_l: integer, 0 <= qnum_l <= qnum_n-1\n",
" qnum_m: inetger, -qnum_l <= qnum_m <= qnum_l\n",
" radius: real, 0 < radius\n",
" theta: real, angle\n",
" phi: real, angle\n",
"\n",
" psi_normsq(qnum_n, qnum_l, qnum_m, radius, theta, phi): real, > 0\n",
" \"\"\"\n",
"\n",
" err_msg = \"n, l and m must be integers with n = 0,1,2,...; l = 0,1,...,n-1; m = -l,...,l\"\n",
" if not all([int(x) == x for x in [qnum_n, qnum_l, qnum_m]]):\n",
" raise ValueError(err_msg)\n",
" if not (qnum_n >= 0 and (0 <= qnum_l <= qnum_n - 1) and -qnum_l <= qnum_m <= qnum_l):\n",
" raise ValueError(err_msg)\n",
"\n",
" Y = sph_harm(qnum_m, qnum_l, theta, phi) # note l, m swap order due to implementation of sph_harm\n",
"\n",
" result = np.abs(big_psi(qnum_n, qnum_l, radius) * Y)**2\n",
"\n",
" return result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's sense-check this quickly. The (reduced) Bohr radius $a_0^*$ is defined to be the the most probable distance between the proton and electron in a hydrogen atom in its ground ($n,l,m = 1,0,0$) state. In this case the spherical harmonic $Y_0^0$ is constant, so we can write $\\psi_{100}$ as a function of $r$ alone. The probability of finding an electron at radius $r$ is the integral of $\\psi_{100}(r)$ over the shell of radius $r$. But since $\\psi_{100}(r)$ is constant on shells, this is simply $(4\\pi r^2)\\psi_{100}(r)$. And indeed when we plot this quantity, we see it has a maximum around the Bohr radius."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f112081f210>]"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# lambda function for the probability an electron is at distance r\n",
"psi_100_r2 = lambda r: 4 * np.pi * (r**2) * psi_normsq(1,0,0,r,0,0)\n",
"\n",
"# plot probability as function of r\n",
"rs = np.linspace(1e-15,1e-9, 1000)\n",
"plt.plot(rs, psi_100_r2(rs))\n",
"\n",
"# plot a vertical line at the Bohr radius\n",
"os = np.linspace(psi_100_r2(rs).min(), psi_100_r2(rs).max(), 1000)\n",
"plt.plot(A0_STAR*np.ones(1000), os, color='red', linestyle='dashed')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's make a method for getting the value of $|\\psi_{nlm}|$ at a point in the $xy$ plane. We use `ai.cs` for easy coordinate changes."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"from ai import cs # coordinate trasnformations\n",
"\n",
"def psi_xy(qnum_n, qnum_l, qnum_m, x, y):\n",
" \"\"\"\n",
" value of psi_normsq in the x-y plane\n",
"\n",
" qnum_n: integer, 0 <= qnum_n\n",
" qnum_l: integer, 0 <= qnum_l <= qnum_n-1\n",
" qnum_m: integer, -qnum_l <= qnum_m <= qnum_l\n",
" x: real\n",
" y: real\n",
"\n",
" psi_xy(qnum_n, qnum_l, qnum_m, x, y): real, > 0\n",
" \"\"\"\n",
"\n",
" radius, theta, phi = cs.cart2sp(x, y, 0)\n",
" result = psi_normsq(qnum_n, qnum_l, qnum_m, radius, theta, phi)\n",
"\n",
" return result\n",
"\n",
"# do xz and yz planes for good measure\n",
"\n",
"def psi_xz(qnum_n, qnum_l, qnum_m, x, z):\n",
" \"\"\"\n",
" qnum_n: integer, 0 <= qnum_n\n",
" qnum_l: integer, 0 <= qnum_l <= qnum_n-1\n",
" qnum_m: integer, -qnum_l <= qnum_m <= qnum_l\n",
" x: real\n",
" z: real\n",
" \n",
" psi_xz(qnum_n, qnum_l, qnum_m, x, z): real, > 0\n",
" \"\"\"\n",
" \n",
" radius, theta, phi = cs.cart2sp(x, 0, z)\n",
" result = psi_normsq(qnum_n, qnum_l, qnum_m, radius, theta, phi)\n",
" \n",
" return result\n",
"\n",
"\n",
"def psi_yz(qnum_n, qnum_l, qnum_m, y, z):\n",
" \"\"\"\n",
" qnum_n: integer, 0 <= qnum_n\n",
" qnum_l: integer, 0 <= qnum_l <= qnum_n-1\n",
" qnum_m: integer, -qnum_l <= qnum_m <= qnum_l\n",
" y: real\n",
" z: real\n",
" \n",
" psi_yz(qnum_n, qnum_l, qnum_m, y, z): real, > 0\n",
" \"\"\"\n",
" \n",
" r, theta, phi = cs.cart2sp(0, y, z)\n",
" result = psi_normsq(qnum_n, qnum_l, qnum_m, radius, theta, phi)\n",
" \n",
" return result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we make and plot the image. First we make a meshgrid of the $xy$ plane at a suitable scale, to which we apply our probability field `psi_xy`. Then we use `matplotlib.pyplot`'s `imshow` method to display the resulting matrix as an image."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"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": [
"npix = 2048 # number of pixels\n",
"scale = 9e-10\n",
"\n",
"qnum_n, qnum_l, qnum_m = 3, 2, 1 # quantum numbers\n",
"\n",
"x_axis = np.linspace(-scale, scale, npix)\n",
"y_axis = np.linspace(-scale, scale, npix)\n",
"\n",
"xx, yy = np.meshgrid(x_axis, y_axis)\n",
"img_data = psi_xy(qnum_n, qnum_l, qnum_m, xx, yy)\n",
"\n",
"fig = plt.imshow(img_data)\n",
"\n",
"# set the axes to invisible\n",
"fig.axes.get_xaxis().set_visible(False)\n",
"fig.axes.get_yaxis().set_visible(False)\n",
"\n",
"#plt.savefig('hydrogen_atom_{}{}{}.png'.format(N,L,M))\n",
"# (uncomment to save file) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can package this into a function and experiment with different quantum numbers and scales."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def show_hydrogen_orbital_image(qnum_n, qnum_l, qnum_m, scale, npix=2048):\n",
" \"\"\"\n",
" shows image of hydrogen orbital with given quantun numbers at a given scale\n",
" \n",
" qnum_n: integer, 0 <= qnum_n\n",
" qnum_l: integer, 0 <= qnum_l <= qnum_n-1\n",
" qnum_m: integer, -qnum_l <= qnum_m <= qnum_l\n",
" scale: real, > 0, 9e-10 is a good starting point for low quantum numbers\n",
" npix: integer, width/height of image (in pixels)\n",
" \"\"\"\n",
"\n",
" x_axis = np.linspace(-scale, scale, npix)\n",
" y_axis = np.linspace(-scale, scale, npix)\n",
"\n",
" xx, yy = np.meshgrid(x_axis, y_axis)\n",
" img_data = psi_xy(qnum_n, qnum_l, qnum_m, xx, yy)\n",
"\n",
" fig = plt.imshow(img_data)\n",
"\n",
" # set the axes to invisible\n",
" fig.axes.get_xaxis().set_visible(False)\n",
" fig.axes.get_yaxis().set_visible(False)\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"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": [
"show_hydrogen_orbital_image(4,2,2,scale=2e-9)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This image is fine for viewing in a notebook, however it does not save well. \n",
"We create a function for a save-friendly image.\n",
"\n",
"We also include an option to select the 'colormap'. Standard matplotlib colormaps are given here: https://matplotlib.org/3.1.0/tutorials/colors/colormaps.html"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def create_image(data, cmap='viridis', filename=None):\n",
" \"\"\"\n",
" Creates (and, optionally, saves) image from numpy data\n",
"\n",
" data: numpy real array, assumed square and non-negative\n",
" cmap: matplotlib colormap\n",
" filename: default None (no save in this case), otherwise expects string saves image as filename\n",
" \"\"\"\n",
" sizes = np.shape(data)\n",
" fig = plt.figure(figsize=(5, 5))\n",
" ax = plt.Axes(fig, [0., 0., 1., 1.])\n",
" ax.set_axis_off()\n",
" fig.add_axes(ax)\n",
" ax.imshow(data, cmap)\n",
" if filename is not None:\n",
" plt.savefig(filename, dpi=sizes[0])\n",
" plt.close()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we combine everything into one function:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def hydrogen_orbital_image(qnum_n, qnum_l, qnum_m, scale, npix=2048, cmap='viridis', save=False):\n",
" \"\"\"\n",
" creates (and, optionally, saves) image of hydrogen orbital with given quantun numbers at a given scale\n",
"\n",
" qnum_n: integer, 0 <= qnum_n\n",
" qnum_l: integer, 0 <= qnum_l <= qnum_n-1\n",
" qnum_m: integer, -qnum_l <= qnum_m <= qnum_l\n",
" scale: real, > 0, 9e-10 is a good starting point for low quantum numbers\n",
" npix: integer, width/height of image (in pixels)\n",
" cmap: matplotlib colormap\n",
" save: boolean, if True saves image with filname in format hydrogen_atom_NLM_scale.png\n",
" \"\"\"\n",
"\n",
" # check quantum numbers are in correct range\n",
" err_msg = \"Quantum numbers n, l and m must be integers with n = 0,1,2,...; l = 0,1,...,n-1; m = -l,...,l\"\n",
" if not all([int(x) == x for x in [qnum_n, qnum_l, qnum_m]]):\n",
" raise ValueError(err_msg)\n",
" if not (qnum_n >= 0 and (0 <= qnum_l <= qnum_n - 1) and -qnum_l <= qnum_m <= qnum_l):\n",
" raise ValueError(err_msg)\n",
"\n",
" x_axis = np.linspace(-scale, scale, npix)\n",
" y_axis = np.linspace(-scale, scale, npix)\n",
"\n",
" xx, yy = np.meshgrid(x_axis, y_axis)\n",
" img_data = psi_xy(qnum_n, qnum_l, qnum_m, xx, yy)\n",
"\n",
" if save:\n",
" filename = 'hydrogen_atom_{}{}{}_{}.png'.format(qnum_n, qnum_l, qnum_m, scale)\n",
" else:\n",
" filename = None\n",
" create_image(img_data, cmap, filename)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"hydrogen_orbital_image(5,3,-1,3e-9)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"hydrogen_orbital_image(2,1,-1,5e-10, cmap='hot')"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"hydrogen_orbital_image(8,5,-3,5e-9, cmap='bone')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Todo\n",
"It would be good to implement an autoscale option that selects an appropriate scale without input from the user. I can think of a hacky way to do this. Perhaps better to use analytic properties of big_psi though?"
]
}
],
"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": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
import numpy as np
import matplotlib.pyplot as plt
from scipy.special import sph_harm, genlaguerre
from ai import cs # coordinate trasnformations
A0_STAR = 5.2946541e-11 # The (reduced) Bohr radius A0_STAR is a constant of the universe
def big_psi(qnum_n, qnum_l, radius):
"""
The radial component of the elctron probability denisty.
qnum_n: integer, 0 <= qnum_n
qnum_l: integer, 0 <= qnum_l <= qnum_n-1
radius: real, 0 < raius
big_psi(qnum_n, qnum_l, radius): real
"""
rho = (2*radius) / (qnum_n*A0_STAR)
L = genlaguerre(qnum_n - qnum_l - 1, 2*qnum_l + 1)(rho)
factorial = lambda x: np.prod(np.arange(1, qnum_n + 1)) # good enough factorial for small numbers
sqrt_term = np.sqrt(((2/qnum_n*A0_STAR)**3) * factorial(qnum_n - qnum_l - 1) / (2*qnum_n*factorial(qnum_n + qnum_l)))
result = sqrt_term * np.exp(-rho/2) * (rho**qnum_l) * L
return result
def psi_normsq(qnum_n, qnum_l, qnum_m, radius, theta, phi):
"""
Multiply the radial component big_psi by the appropriate spherical harmonic and take the norm-square.
qnum_n: integer, 0 <= qnum_n
qnum_l: integer, 0 <= qnum_l <= qnum_n-1
qnum_m: inetger, -qnum_l <= qnum_m <= qnum_l
radius: real, 0 < radius
theta: real, angle
phi: real, angle
psi_normsq(qnum_n, qnum_l, qnum_m, radius, theta, phi): real, > 0
"""
err_msg = "n, l and m must be integers with n = 0,1,2,...; l = 0,1,...,n-1; m = -l,...,l"
if not all([int(x) == x for x in [qnum_n, qnum_l, qnum_m]]):
raise ValueError(err_msg)
if not (qnum_n >= 0 and (0 <= qnum_l <= qnum_n - 1) and -qnum_l <= qnum_m <= qnum_l):
raise ValueError(err_msg)
Y = sph_harm(qnum_m, qnum_l, theta, phi) # note l, m swap order due to implementation of sph_harm
result = np.abs(big_psi(qnum_n, qnum_l, radius) * Y)**2
return result
def psi_xy(qnum_n, qnum_l, qnum_m, x, y):
"""
value of psi_normsq in the x-y plane
qnum_n: integer, 0 <= qnum_n
qnum_l: integer, 0 <= qnum_l <= qnum_n-1
qnum_m: integer, -qnum_l <= qnum_m <= qnum_l
x: real
y: real
psi_xy(qnum_n, qnum_l, qnum_m, x, y): real, > 0
"""
radius, theta, phi = cs.cart2sp(x, y, 0)
result = psi_normsq(qnum_n, qnum_l, qnum_m, radius, theta, phi)
return result
def create_image(data, cmap='viridis', filename=None):
"""
Creates (and, optionally, saves) image from numpy data
data: numpy real array, assumed square and non-negative
cmap: matplotlib colormap
filename: default None (no save in this case), otherwise expects string saves image as filename
"""
sizes = np.shape(data)
fig = plt.figure(figsize=(5, 5))
ax = plt.Axes(fig, [0., 0., 1., 1.])
ax.set_axis_off()
fig.add_axes(ax)
ax.imshow(data, cmap)
if filename is not None:
plt.savefig(filename, dpi=sizes[0])
plt.close()
def hydrogen_orbital_image(qnum_n, qnum_l, qnum_m, scale, npix=2048, cmap='viridis', save=False):
"""
creates (and, optionally, saves) image of hydrogen orbital with given quantun numbers at a given scale
qnum_n: integer, 0 <= qnum_n
qnum_l: integer, 0 <= qnum_l <= qnum_n-1
qnum_m: integer, -qnum_l <= qnum_m <= qnum_l
scale: real, > 0, 9e-10 is a good starting point for low quantum numbers
npix: integer, width/height of image (in pixels)
cmap: matplotlib colormap
save: boolean, if True saves image with filname in format hydrogen_atom_NLM_scale.png
"""
# check quantum numbers are in correct range
err_msg = "Quantum numbers n, l and m must be integers with n = 0,1,2,...; l = 0,1,...,n-1; m = -l,...,l"
if not all([int(x) == x for x in [qnum_n, qnum_l, qnum_m]]):
raise ValueError(err_msg)
if not (qnum_n >= 0 and (0 <= qnum_l <= qnum_n - 1) and -qnum_l <= qnum_m <= qnum_l):
raise ValueError(err_msg)
x_axis = np.linspace(-scale, scale, npix)
y_axis = np.linspace(-scale, scale, npix)
xx, yy = np.meshgrid(x_axis, y_axis)
img_data = psi_xy(qnum_n, qnum_l, qnum_m, xx, yy)
if save:
filename = 'hydrogen_atom_{}{}{}_{}.png'.format(qnum_n, qnum_l, qnum_m, scale)
else:
filename = None
create_image(img_data, cmap, filename)
# TODO: it would be good to implenent an autoscale option to select an appropriate scale for the orbital image without input from the user.
# I can think of a hacky way to do this. Perhaps better to use analytic properties of big_psi though?
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