The degenerate parametric oscillator and Ince's equation

Ricardo Cordero-Sotos; Sergei Suslov

doi:10.1088/1751-8113/44/1/015101

The degenerate parametric oscillator and Ince's equation

Ricardo Cordero-Sotos, Sergei Suslov

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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.

Original language	English (US)
Article number	015101
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	44
Issue number	1
DOIs	https://doi.org/10.1088/1751-8113/44/1/015101
State	Published - Jan 7 2011

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modeling and Simulation
Mathematical Physics
General Physics and Astronomy

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10.1088/1751-8113/44/1/015101

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AB - 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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The degenerate parametric oscillator and Ince's equation

Abstract

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