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On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations (1304.3982v2)
Published 15 Apr 2013 in quant-ph, math-ph, and math.MP
Abstract: We study the solvability of the time-independent matrix Schr\"odinger 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.