How to use the hame module
In a typical usage, you will call a routine of the hame library to compute a matrix element.
Some examples are given below. A Python script containing these examples is available here.
One-photon matrix element
To compute numerically the dipole matrix element between the 1S and 2P states of the hydrogen atom, you may use:
>>> import hame
>>> n, l = 1, 0
>>> nprime, lprime = 2, 1
>>> nsup = 20
>>> print('<',n,l,'| z |',nprime,lprime,'> from Gordon formula :',hame.gordon_formula(n, l, nprime, lprime))
< 1 0 | z | 2 1 > from Gordon formula : 0.7449355390278027
>>> print('<',n,l,'| z |',nprime,lprime,'> from numerics :',hame.compute_dipole_matrix_element(n, l, nprime, lprime, nsup))
< 1 0 | z | 2 1 > from numerics : 0.7449355390278033