Entropy and information of a spinless charged particle in time-varying magnetic fields

摘要

We calculate the Fisher information (F-r and F-p) and the Shannon entropies (S-r and S-p) of a spinless charged particle in three different configurations of time-varying magnetic field, B(t). To do so, we first obtain the exact wave functions for a general time-dependent system by using a dynamical invariant method. By considering the solutions for n = m = 0, we were able to obtain the expressions of F-r, F-p, S-r, and S-p in terms of a c-number quantity, rho, which has to be a real solution of the Milne-Pinney equation. We observe that the inequality FrFp <= 16 holds for the systems considered. We also observed squeezing phenomenon in momentum or/and coordinate spaces with increasing time. Published by AIP Publishing.