Study of the generalized parametric oscillator

Chi‐Fai Lo

In this paper we derive the coherent-state propagator of a generalized time-dependent parametric oscillator using the Lie algebraic approach. The method is simple and gives the same results as those obtained by the path integral approach. Furthermore, this Lie algebraic approach can be easily generalized to a time-dependent many-body system once the algebraic structure of its Hamiltonian is identified.

Paul Kinsler

Вадим Васильевич Борзов

Ricardo Cordero–Soto, Sergeĭ K. Suslov

We construct Green's function for the quantum degenerate parametric oscillator in the coordinate representation in terms of standard solutions of Ince's equation in a framework of a general approach to variable quadratic Hamiltonians. Exact time-dependent wavefunctions and their connections with dynamical invariants and SU (1, 1) group are also discussed. An extension to the degenerate parametric oscillator with time-dependent amplitude and phase is also mentioned.

Matthew T. Rakher, Kartik A. Srinivasan

I. A. Pedrosa, I. Guedes

By using canonical and unitary transformations and the Lewis–Riesenfeld invariant method, the generalized invariant and the exact Schrödinger wave functions for a time-dependent parametric oscillator with and without an inverse quadratic potential are obtained.