On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations
Quantum Physics
2013-10-30 v2 Mathematical Physics
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.
Keywords
Cite
@article{arxiv.1304.3982,
title = {On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations},
author = {Yao-Zhong Zhang},
journal= {arXiv preprint arXiv:1304.3982},
year = {2013}
}
Comments
LaTex 16 pages. Some modifications and addition of references. Version to appear in J. Math. Phys