Generalized Rayleigh-Schroedinger perturbation theory as a method of linearization of the so called quasi-exactly solvable models
Miloslav Znojil
Abstract
Sextic oscillator in D dimensions is considered as a typical quasi-exactly solvable (QES) model. Usually, its QES N-plets of bound states have to be computed using the coupled Magyari's nonlinear algebraic equations. We propose and describe an alternative linear method which is N-independent and works with power series in 1/(D). Main merit: simultaneous exact solvability (for all the QES states) in the first two leading orders (the degeneracy is completely removed, the unperturbed spectrum is equidistant). An additional merit: All the perturbation corrections are given by explicit matrix formulae in integer arithmetics (there are no rounding errors).
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