
Symmetry in Nonlinear Mathematical Physics  2009
Sergiy Dolya (B. Verkin Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine)
Quasiexactly solvable models, quadratic Lie algebras and special functions
Abstract:
We construct finitedimensional 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. These findings are used in
studies of quasiexactly solvable (QES) models in quantum mechanics. In particular, we show that the known twophoton Rabi Hamiltonian
becomes QES at certain values of parameters. In doing so, there are two underlying Lie algebra, both of them being quadratic.
Presentation

