def test_psi_nlm():
r = S('r')
phi = S('phi')
theta = S('theta')
assert (Psi_nlm(1, 0, 0, r, phi, theta) == exp(-r) / sqrt(pi))
assert (Psi_nlm(2, 1, -1, r, phi, theta)) == S.Half * exp(-r / (2)) * r \
* (sin(theta) * exp(-I * phi) / (4 * sqrt(pi)))
assert (Psi_nlm(3, 2, 1, r, phi, theta, 2) == -sqrt(2) * sin(theta) \
* exp(I * phi) * cos(theta) / (4 * sqrt(pi)) * S(2) / 81 \
* sqrt(2 * 2 ** 3) * exp(-2 * r / (3)) * (r * 2) ** 2)
def test_psi_nlm():
r = S("r")
phi = S("phi")
theta = S("theta")
assert Psi_nlm(1, 0, 0, r, phi, theta) == exp(-r) / sqrt(pi)
assert (Psi_nlm(
2, 1, -1, r, phi,
theta)) == S.Half * exp(-r / (2)) * r * (sin(theta) * exp(-I * phi) /
(4 * sqrt(pi)))
assert (Psi_nlm(3, 2, 1, r, phi, theta, 2) == -sqrt(2) * sin(theta) *
exp(I * phi) * cos(theta) / (4 * sqrt(pi)) * S(2) / 81 *
sqrt(2 * 2**3) * exp(-2 * r / (3)) * (r * 2)**2)
theta = Symbol("theta", real=True)
Z = Symbol("Z", positive=True, integer=True, nonzero=True)
"""
# Psi_nlm(n, l, m, r, phi, theta, Z)
n, l, m quantum numbers ‘n’, ‘l’ and ‘m’
r radial coordinate
phi azimuthal angle
theta polar angle
Z atomic number (1 for Hydrogen, 2 for Helium, …)
"""
n = argv.get("n", 3)
l = argv.get("l", 1)
m = argv.get("m", 0)
density = argv.get("density", 1.0)
f = Psi_nlm(n, l, m, r, phi, theta, 1)
print("psi(r, phi, theta) =", f)
vmin = -15. * n
vmax = 15. * n
N = 32
delta = (vmax - vmin) / N
vals = list(numpy.arange(vmin, vmax, delta))
nx = ny = nz = len(vals)
data = []
for x in vals:
for y in vals:
for z in vals:
if abs(x) < 1e-6: