Even and Odd Coherent States for Time-Dependent Harmonic Oscillator**The project supported in part by National Natural Science Foundation of China and the Doctoral Education Fund of the Education Ministry of China

Abstract

The dynamical invariant for a general time-dependent harmonic oscillator is constructed by making use of two linearly independent solutions to the classical equation of motion. In terms of this dynamical invariant we define the time-dependent creation and annihilation operators and relevantly introduce even and odd coherent states for time-dependent harmonic oscillator. The mathematical and quantum statistical properties of these states are discussed in detail. The harmonic oscillator with periodically varying frequency is treated as a demonstration of our general approach.