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Acta Physica Sinica

TIME EVOLUTION AND SQUEEZED STATES OF A TIME-DEPEDENT OSCILLATOR SYSTEM

Dang Lan-fen, 河北大学物理系，保定 071002

Published Jan 1, 1998• 1 citation
Publisher

Abstract

In this paper are discussed the time evolution and squeezed states of a time-depedent oscillator system. We obtain closed formulas for the time evolution of quantum states and the evolution operator of the system by selecting proper Hermitian invariant operator. We derive the condition generating squeezed states and obtain that the drive part does not influence the squeezed states of the system.

DOI
10.7498/aps.47.1071

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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.
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