test_hydrogen.py 文件源码

def test_wavefunction():
    a = 1/Z
    R = {
        (1, 0): 2*sqrt(1/a**3) * exp(-r/a),
        (2, 0): sqrt(1/(2*a**3)) * exp(-r/(2*a)) * (1 - r/(2*a)),
        (2, 1): S(1)/2 * sqrt(1/(6*a**3)) * exp(-r/(2*a)) * r/a,
        (3, 0): S(2)/3 * sqrt(1/(3*a**3)) * exp(-r/(3*a)) *
        (1 - 2*r/(3*a) + S(2)/27 * (r/a)**2),
        (3, 1): S(4)/27 * sqrt(2/(3*a**3)) * exp(-r/(3*a)) *
        (1 - r/(6*a)) * r/a,
        (3, 2): S(2)/81 * sqrt(2/(15*a**3)) * exp(-r/(3*a)) * (r/a)**2,
        (4, 0): S(1)/4 * sqrt(1/a**3) * exp(-r/(4*a)) *
        (1 - 3*r/(4*a) + S(1)/8 * (r/a)**2 - S(1)/192 * (r/a)**3),
        (4, 1): S(1)/16 * sqrt(5/(3*a**3)) * exp(-r/(4*a)) *
        (1 - r/(4*a) + S(1)/80 * (r/a)**2) * (r/a),
        (4, 2): S(1)/64 * sqrt(1/(5*a**3)) * exp(-r/(4*a)) *
        (1 - r/(12*a)) * (r/a)**2,
        (4, 3): S(1)/768 * sqrt(1/(35*a**3)) * exp(-r/(4*a)) * (r/a)**3,
    }
    for n, l in R:
        assert simplify(R_nl(n, l, r, Z) - R[(n, l)]) == 0