2010•Journal of Physics A Mathematical and TheoreticalOpen access

The degenerate parametric oscillator and Ince's equation

Ricardo Cordero–Soto, Sergeĭ K. Suslov

Abstract

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.

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Key concepts: Degenerate energy levels, Parametric oscillator, Parametric statistics, Physics, Mathematical analysis, Mathematics, Mathematical physics, Quantum mechanics