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arXiv · 0803.2929

Quasi-exactly solvable models based on special functions

S. N. Dolya
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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.

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BibTeXRIS

S. N. Dolya. 2008-03-20. Quasi-exactly solvable models based on special functions. https://doi.org/10.1063/1.2905153

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