I am still puzzled by the results that I obtain with GTPack for the basis functions of irreps of point groups, in particular for the two-dimensional irrep E” of group D3h.
I have followed your comments in a previous post. I see your point and I can reproduce your results, but unfortunately they still don’t solve my problem, because the functions that you propose:
cartf1 –> -y z
cartf2 –> +x z
do not verify the canonical definition of representation basis functions that you introduce in the book –> eq. (5.47) (see an image of my notebook below). They satisfy instead another similar but different relation that you also write later on in the book –> eq. (5.68), but this is not typically the property that one wants!
This is really disturbing, because in every group theory reference one can find that (xz,yz) are indeed the basis functions (with definition eq. (5.47)) of irrep E” of D3h.
Could there be any issue with the way the operator GTTransformationOperator is defined within GTPack?
An independent intriguing result I have found when working on the above task is some difference in the output of commands GTProjectionOperator and GTWignerProjectionOperator, when applied to e.g. an spherical harmonic (see also at the end of my notebook). Here, I am not sure whether this difference
is relevant or not, since I do not know the internal workings of both commands, but I point to it anyway.
Can you help me with this mess, please? Am I misinterpreting something?