On Wed, Mar 9, 2022 at 9:04 PM Gerson J. Ferreira <[email protected]> wrote: > > To write the formatted symbols I use the "Tex for Gmail" extension (only > works in Chrome), which allows me to use Latex expressions in the email and > it compiles using Unicode text or PNG images. Here I'm using the unicode > option. > > Regarding your question, we can say that the numerical QE matrix is A, while > B is the representation that I want to work with. So I know both and the only > unknown is U. For an algorithm on how to find U, please check: > >> M. Mozrzymas, M. Studziński, and M. Horodecki >> Explicit constructions of unitary transformations between equivalent >> irreducible representations >> J. Phys. A. 47, 505203 (2014). > > > My problem is that I want to use the QE wave-functions to do some > calculation, but it needs to be in the B representation, so I need to find > the similarity transformation (or basis transformation) U that takes A to B, > so I can apply it to the QE wave-functions. As I said above, I have B (it's > my choice of basis) and I need QE to calculate A, then my code finds U.
Taking your aforementioned 2-dimensional matrices as an example, based on the tricks given here [1-2], I obtained the method as shown in the attachment. [1] https://mathematica.stackexchange.com/questions/98514/finding-a-unitary-matrix-in-mathematica [2] https://math.stackexchange.com/questions/4199837/find-a-matrix-for-a-unitary-transform-between-matrices-or-prove-that-there-is-no/4199915 Regards, Hongyi
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