The degenerate parametric oscillator and Ince's equation

Ricardo Cordero-Sotos, Sergei Suslov

Research output: Contribution to journalArticle

13 Citations (Scopus)

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 languageEnglish (US)
Article number015101
JournalJournal of Physics A: Mathematical and Theoretical
Volume44
Issue number1
DOIs
StatePublished - Jan 7 2011

Fingerprint

Parametric oscillators
parametric amplifiers
Hamiltonians
Wave functions
Green's function
Green's functions
Invariant

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modeling and Simulation
  • Statistics and Probability

Cite this

The degenerate parametric oscillator and Ince's equation. / Cordero-Sotos, Ricardo; Suslov, Sergei.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 44, No. 1, 015101, 07.01.2011.

Research output: Contribution to journalArticle

@article{f728d5c77a3a4d89a3f353fd8921dafb,
title = "The degenerate parametric oscillator and Ince's equation",
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.",
author = "Ricardo Cordero-Sotos and Sergei Suslov",
year = "2011",
month = "1",
day = "7",
doi = "10.1088/1751-8113/44/1/015101",
language = "English (US)",
volume = "44",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "1",

}

TY - JOUR

T1 - The degenerate parametric oscillator and Ince's equation

AU - Cordero-Sotos, Ricardo

AU - Suslov, Sergei

PY - 2011/1/7

Y1 - 2011/1/7

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=78751542986&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78751542986&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/44/1/015101

DO - 10.1088/1751-8113/44/1/015101

M3 - Article

AN - SCOPUS:78751542986

VL - 44

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 1

M1 - 015101

ER -