Quasi-exactly solvable quartic Bose Hamiltonians

Details Quasi-exactly solvable quartic Bose Hamiltonians Quasi-exactly solvable quartic Bose Hamiltonians

2001-06-24

arxiv.org/abs/quant-ph/0106134v2

J.Phys.A34:5955-5968,2001

Physics

Quantum Physics

21 pages, REVTeX 3.0, no figures. In v.2 couple of misprints in English corrected. To be published in J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/34/30/307

We consider Hamiltonians, which are even polynomials of the forth order with the respect to Bose operators. We find subspaces, preserved by the action of Hamiltonian These subspaces, being finite-dimensional, include, nonetheless, states with an \QTR{it}{infinite} number of quasi-particles, corresponding to the original Bose operators. The basis functions look rather simple in the coherent state representation and are expressed in terms of the degenerate hypergeometric function with respect to the complex variable labeling the representation. In some particular degenerate cases they turn (up to the power factor) into the trigonometric or hyperbolic functions, Bessel functions or combinations of the exponent and Hermit polynomials. We find explicitly the relationship between coefficients at different powers of Bose operators that ensure quasi-exact solvability of Hamiltonian.

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