Berry phases in the quantum state of the isotropic harmonic oscillator with time-dependent frequency and boundary conditions

Abstract

The problem of the isotopic harmonic oscillator of time-dependent frequency confined in a spherical box with time-dependent radius is studied. We show that the exact solution and the Lewis invariant operator can be obtained by performing two consecutive gauge transformations on the time-dependent Schrodinger equation. On the basis of the exact solution the non-adiabatic Berry phases for the system are calculated.