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| from sympy.core import symbols, Rational, Function, diff | |
| from sympy.physics.sho import R_nl, E_nl | |
| from sympy.simplify.simplify import simplify | |
| 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 | |