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Title: Full spectrum of the two-photon and the two-mode quantum Rabi models

This paper is concerned with the rigorous analytical determination of the spectrum of the two-photon and the two-mode quantum Rabi models. To reach this goal, we exploit the hidden symmetries in these models by means of the unitary and similarity transformations in addition to the Bargmann-Fock space description. In each case, the purely quantum mechanical problem of the Rabi model studied is reduced to solutions for differential equations. This eventually gives a third-order differential equation for each of these models, which is reduced to a second-order differential equation by additional transformations. The analytical expressions of the wave functions describing the energy levels are obtained in terms of the confluent hypergeometric functions.
Authors:
;  [1]
  1. Unité de Recherche en Physique Théorique (URPT), Institut de Mathématiques et de Sciences Physiques (IMSP), Université d'Abomey-Calavi - UAC, 01 BP 613 Porto-Novo (Benin)
Publication Date:
OSTI Identifier:
22305857
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 10; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIFFERENTIAL EQUATIONS; ENERGY LEVELS; HYPERGEOMETRIC FUNCTIONS; MATHEMATICAL SOLUTIONS; PHOTONS; QUANTUM MECHANICS; SYMMETRY; WAVE FUNCTIONS