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
