def test_sho_R_nl():
omega, r = symbols('omega r')
l = symbols('l', integer=True)
u = Function('u')
# check that it obeys the Schrodinger equation
for n in range(5):
schreq = (-diff(u(r), r, 2) / 2 + (
(l * (l + 1)) /
(2 * r**2) + omega**2 * r**2 / 2 - E_nl(n, l, omega)) * u(r))
result = schreq.subs(u(r), r * R_nl(n, l, omega / 2, r))
assert simplify(result.doit()) == 0
def test_energy():
n, l, hw = symbols('n l hw')
assert simplify(E_nl(n, l, hw) - (2 * n + l + Rational(3, 2)) * hw) == 0
from sympy.physics.qho_1d import E_n, psi_n
from sympy.physics.sho import E_nl, R_nl
from sympy import var
var("x m omega")
var("r nu l")
x, y, z = symbols('x, y, z')
E_n(x, omega)
psi_n(2, x, m, omega)
E_nl(x, y, z)
R_nl(1, 0, 1, r)
R_nl(2, l, 1, r)