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arXiv · 1304.3982

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

Yao-Zhong Zhang
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Abstract

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.

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Yao-Zhong Zhang. 2013-10-09. On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations. https://doi.org/10.1063/1.4826356

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