22 lines
693 B
Python
22 lines
693 B
Python
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from sympy.core import symbols, Rational, Function, diff
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from sympy.physics.sho import R_nl, E_nl
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from sympy.simplify.simplify import simplify
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def test_sho_R_nl():
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omega, r = symbols('omega r')
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l = symbols('l', integer=True)
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u = Function('u')
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# check that it obeys the Schrodinger equation
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for n in range(5):
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schreq = ( -diff(u(r), r, 2)/2 + ((l*(l + 1))/(2*r**2)
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+ omega**2*r**2/2 - E_nl(n, l, omega))*u(r) )
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result = schreq.subs(u(r), r*R_nl(n, l, omega/2, r))
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assert simplify(result.doit()) == 0
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def test_energy():
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n, l, hw = symbols('n l hw')
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assert simplify(E_nl(n, l, hw) - (2*n + l + Rational(3, 2))*hw) == 0
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