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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
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