Analytical eigenstates for the quantum Rabi model
arXiv:1305.6782 · doi:10.1088/1751-8113/46/41/415302
Abstract
We develop a method to find analytical solutions for the eigenstates of the quantum Rabi model. These include symmetric, anti-symmetric and asymmetric analytic solutions given in terms of the confluent Heun functions. Both regular and exceptional solutions are given in a unified form. In addition, the analytic conditions for determining the energy spectrum are obtained. Our results show that conditions proposed by Braak [Phys. Rev. Lett. \textbf{107}, 100401 (2011)] are a type of sufficiency condition for determining the regular solutions. The well-known Judd isolated exact solutions appear naturally as truncations of the confluent Heun functions.
15 pages, 3 figure, to appear in J. Phys. A