1304.3982 (Yao-Zhong Zhang)

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

Yao-Zhong Zhang

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.

View original: http://arxiv.org/abs/1304.3982