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Title: On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations

We study the solvability of the time-independent matrix Schrödinger differential equations of the quantum Rabi model and its 2-photon and two-mode generalizations in Bargmann Hilbert spaces of entire functions. We show that the Rabi model and its 2-photon and two-mode analogs are quasi-exactly solvable. We derive the exact, closed-form expressions for the energies and the allowed model parameters for all the three cases in the solvable subspaces. Up to a normalization factor, the eigenfunctions for these models are given by polynomials whose roots are determined by systems of algebraic equations.
Authors:
 [1]
  1. School of Mathematics and Physics, The University of Queensland, Brisbane, Qld 4072 (Australia)
Publication Date:
OSTI Identifier:
22217886
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 10; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; EIGENFUNCTIONS; EIGENVALUES; EXACT SOLUTIONS; HILBERT SPACE; MATRICES; PHOTONS; POLYNOMIALS; SCHROEDINGER EQUATION