def test_wavefunction(): Psi = { 0: (1/sqrt(2 * pi)), 1: (1/sqrt(2 * pi)) * exp(I * x), 2: (1/sqrt(2 * pi)) * exp(2 * I * x), 3: (1/sqrt(2 * pi)) * exp(3 * I * x) } for n in Psi: assert simplify(wavefunction(n, x) - Psi[n]) == 0
def test_orthogonality(n=1): # Maximum "n" which is tested: for i in range(n + 1): for j in range(i+1, n+1): assert integrate( wavefunction(i, x) * wavefunction(j, x), (x, 0, 2 * pi)) == 0
def test_norm(n=1): # Maximum "n" which is tested: for i in range(n + 1): assert integrate( wavefunction(i, x) * wavefunction(-i, x), (x, 0, 2 * pi)) == 1