Berry phases in the quantum state of the Isotropic harmonic oscillator with Time-dependent frequency and Boundary conditions

摘要

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.