Quasi-exactly solvable models based on special functions

Abstract

We suggest a systematic method of extension of quasi-exactly solvable (QES) systems. We construct finite-dimensional subspaces on the basis of special functions (hypergeometric, Airy, Bessel ones) invariant with respect to the action of differential operators of the second order with polynomial coefficients. As a example of physical applications, we show that the known two-photon Rabi Hamiltonian becomes quasi-exactly solvable at certain values of parameters when it can be expressed in terms of corresponding QES operators related to the hypergeometric function.

15 pages. Typos corrected

References in corpus (2)

• Exact isolated solutions for the two-photon Rabi Hamiltonian
• Conditional symmetry and spectrum of the one-dimensional Schrödinger equation

Cited by in corpus (5)

• The quantum Rabi model: solution and dynamics
• Symmetric Rotating Wave Approximation for the Generalized Single-Mode Spin-Boson System
• Quadratic Lie algebras and quasi-exact solvability of the two-photon Rabi Hamiltonian
• Quasi-exact solvability, resonances and trivial monodromy in ordinary differential equations
• Loss of integrability in a system with two-photon interactions