dipole_mat_elem_fix

[allaquan]

Hello,

I changed the "getDipoleMatrixElement" function, as when I was using it some results would differ by -1. This is because the notation / documentaiton for initial and final states are flipped. For example on the website:

transition 5 S_{1/2} m_j=-0.5 -> 5 P_{3/2} m_j=-1.5

for laser driving sigma- transition

print(atom.getDipoleMatrixElement(5,0,0.5,-0.5,5,1,1.5,-1.5,-1))

Here the initial states, (5,0,0.5,-0.5) should be on the right side i.e. the ket, whereas the final states (5,1,1.5,-1.5) should be on the left side i.e. the bra, however using this notation the ordering is flipped which causes an additional -1 factor.

Consequently, the matching q should also be multiplied by -1 to make it work with the function "getSphericalDipoleMatrixElement"

In theory, q should not be multiplied by -1, however the "getSphericalDipoleMatrixElement" function is implemented (I believe) incorrectly when compared to the Wigner Eckart theorem, as the q should not be negative in the expression

return (-1) ** (j1 - mj1) * Wigner3j(j1, 1, j2, -mj1, -q, mj2)

However, I thought it was best not to alter that function since there were many dependencies on it, and I did not want to break other parts of the code that might have already accounted for this alteration.

Thanks