The Degenerate Parametric Oscillator and Ince's Equation
Ricardo Cordero-Soto, Sergei K. Suslov
TL;DR
This paper develops a Green's function for the quantum degenerate parametric oscillator using Ince's equation solutions, linking it with wave functions, dynamical invariants, and SU(1,1) symmetry.
Contribution
It introduces a novel method to construct Green's functions for the quantum oscillator via Ince's equation, enhancing understanding of its quantum dynamics.
Findings
Green's function expressed in terms of Ince's equation solutions
Exact time-dependent wave functions derived
Connections with dynamical invariants and SU(1,1) group established
Abstract
We construct Green's function for the quantum degenerate parametric oscillator in terms of standard solutions of Ince's equation in a framework of a general approach to harmonic oscillators. Exact time-dependent wave functions and their connections with dynamical invariants and SU(1,1) group are also discussed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.