On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field
arXiv:2207.02933 · doi:10.1063/5.0106709
Abstract
A Charged harmonic oscillator in a magnetic field, Landau problems, and an oscillator in a noncommutative space, share the same mathematical structure in their Hamiltonians. We have considered a two-dimensional anisotropic harmonic oscillator (AHO) with arbitrarily time-dependent parameters (effective mass and frequencies), placed in an arbitrarily time-dependent magnetic field. A class of quadratic invariant operators (in the sense of Lewis and Riesenfeld) have been constructed. The invariant operators () have been reduced to a simplified representative form by a linear canonical transformation (the group ). An orthonormal basis of the Hilbert space consisting of the eigenvectors of is obtained. In order to obtain the solutions of the time-dependent Schrödinger equation corresponding to the system, both the geometric and dynamical phase-factors are constructed. Peres-Horodecki Separability Criterion for the bipartite coherent states corresponding to our system has been demonstrated.
arXiv commentarXiv admin note: text overlap with arXiv:2206.10599
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