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Acta Physica Sinica

Time Evolution and Berry Phases of a Time－Dependent Oscillator in Fin ite－Dimensional Hilbert Space

Li Zhi-Jian, Cheng Jian－gang, Liang Jiu-Qing, 山西大学物理系,太原030006

Published Jan 1, 2000• 1 citation
Publisher

Abstract

In this paper we investigate the time evolution of a time－dependent oscillator in finite－dimensional Hilbert space. By performing appropriate time－dependent gauge transformation closed formulas for the time evolution of quantum states an d Berry phases are obtained. Finally we discuss the influence of the driving te rm in the Hamiltonian on the squeezed feature of coherent states.

DOI
10.7498/aps.49.11

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In this paper we investigate the time evolution of a time－dependent oscillator in finite－dimensional Hilbert space. By performing appropriate time－dependent gauge transformation closed formulas for the time evolution of quantum states an d Berry phases are obtained. Finally we discuss the influence of the driving te rm in the Hamiltonian on the squeezed feature of coherent states.
Abstract The problem of a harmonic oscillator of time dependent frequency confined in a one dimensional infinite square well with a moving wall is studied.It is shown that the exact solution and the Lewis invariant operator of the system can be obtained by performing two consecutive gauge transformations on the time dependent Schrdinger equation.On the basis of the exact solution the Berry phases for the system are calculated by using the geometric concepts such as the geometric distance and geometric length of the curve.
We study the time evolution of a class of exactly solvable time-dependent quantum systems with a time-dependent Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators with the help of the invariant Hermitian operator. The exact common solutions of the Schrödinger equations for both the SU(1,1) and SU(2) systems are obtained in terms of eigenstates of the invariant operator. The adiabatic and non-adiabatic Berry phases are calculated with the exact solutions. Moreover, we derive an explicit time-evolution operator which is used to investigate the time-dependent two-photon squeezing states and SU(2) squeezing states. The squeezing properties of the time-dependent SU(1,1) coherent states are also discussed.
The problem of a harmonic oscillator of time-dependent frequency confined in a one-dimensional infinite square well with a moving wall is studied.It is shown that the exact solution and the Lewis invariant operator of the system can be obtained by performing two consecutive gauge transformations on the time-dependent Schrdinger equation.On the basis of the exact solution the Berry phases for the system are calculated by using the geometric concepts such as the geometric distance and geometric length of the curve.