Generalized Rayleigh-Schroedinger perturbation theory as a method of linearization of the so called quasi-exactly solvable models

Details Generalized Rayleigh-Schroedinger perturbation theory as a method of linearization of the so called quasi-exactly solvable models Generalized Rayleigh-Schroedinger perturbation theory as a method of linearization of the so called quasi-exactly solvable models

2001-01-15

arxiv.org/abs/math-ph/0101015v2

Proc. Inst. Math. (NAS Ukraine) 43, Part 2 (2002) 777 - 781

Physics

Mathematical Physics

9 pages for proceedings of the 4th Int. Conf. ``Symmetry in Nonlinear Mathematical Physics" (July 9 - 15, 2001, Kyiv, Ukraine)

Scientific paper

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/\sqrt(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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