Equivalent quantum systems

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 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 it will be achieved in the theory of control quantum systems.