TIME DEPENDENT HARMONIC OSCILLATORS AND SQUEEZED STATES

Nuri Ünal

Kazutaka G. Nakamura

Xiaoguang Wang

Bancha Kirdmanee, Surarit Pepore, Bodinchat Sukbot

We demonstrate that the use of a space-time transformation in path integral can simplify the calculation of the propagator for a harmonic oscillator with time-dependent mass and frequency. We show that such a propagator can be easily obtained from the unit mass and frequency propagator in the new space-time coordinate systems. Two cases of harmonic oscillator with time-dependent mass, which exact propagator can be evaluated, are investigated.

U Yl

The problem of time evolution and squeezed states of the generalized quadratic time-dependent harmonic oscillator is studied by making use of the time-evolution operator approach. Then, the squeezed states and high-n squeezed states of the driven harmonic oscillator with strongly pulsating mass are constructed. Finally, we show how the squeezed-coherent states and high-n squeezed-coherent states, which preserve the minimum uncertainty codition, can be generated.

I. A. PEDROSA, I. GUEDES

We discuss the extension of the Lewis and Riesenfeld method of solving the time-dependent Schrödinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized time-dependent inverted harmonic oscillator. As a special case, we consider a generalized inverted oscillator with constant frequency and exponentially increasing mass.