Equivalent quantum systems
General Physics
2023-08-28 v1
Abstract
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects the Hamiltonian operators associated with each quantum system. This bridge allows us to connect different quantum systems, in such a way that studying one of them allows to understand the other through a gauge transformation. Furthermore, we included the case where the Hamiltonian operator can be time-dependent. An application for this construction will be achieved in the theory of control quantum systems.
Cite
@article{arxiv.2308.12977,
title = {Equivalent quantum systems},
author = {M. Caruso},
journal= {arXiv preprint arXiv:2308.12977},
year = {2023}
}