Quasi-exactly solvable models based on special functions

Details Quasi-exactly solvable models based on special functions Quasi-exactly solvable models based on special functions

2008-03-20

arxiv.org/abs/0803.2929v2

J. Math. Phys. 49, 053524 (2008)

Physics

Mathematical Physics

15 pages. Typos corrected

Scientific paper

10.1063/1.2905153

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.

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