test_clebsch_gordan.py 文件源码

def test_dot_rota_grad_SH():
    theta, phi = symbols("theta phi")
    assert dot_rot_grad_Ynm(1, 1, 1, 1, 1, 0) !=  \
        sqrt(30)*Ynm(2, 2, 1, 0)/(10*sqrt(pi))
    assert dot_rot_grad_Ynm(1, 1, 1, 1, 1, 0).doit() ==  \
        sqrt(30)*Ynm(2, 2, 1, 0)/(10*sqrt(pi))
    assert dot_rot_grad_Ynm(1, 5, 1, 1, 1, 2) !=  \
        0
    assert dot_rot_grad_Ynm(1, 5, 1, 1, 1, 2).doit() ==  \
        0
    assert dot_rot_grad_Ynm(3, 3, 3, 3, theta, phi).doit() ==  \
        15*sqrt(3003)*Ynm(6, 6, theta, phi)/(143*sqrt(pi))
    assert dot_rot_grad_Ynm(3, 3, 1, 1, theta, phi).doit() ==  \
        sqrt(3)*Ynm(4, 4, theta, phi)/sqrt(pi)
    assert dot_rot_grad_Ynm(3, 2, 2, 0, theta, phi).doit() ==  \
        3*sqrt(55)*Ynm(5, 2, theta, phi)/(11*sqrt(pi))
    assert dot_rot_grad_Ynm(3, 2, 3, 2, theta, phi).doit() ==  \
        -sqrt(70)*Ynm(4, 4, theta, phi)/(11*sqrt(pi)) + \
        45*sqrt(182)*Ynm(6, 4, theta, phi)/(143*sqrt(pi))