Perturbation method for non-square Hamiltonians and its application to polynomial oscillators

Details Perturbation method for non-square Hamiltonians and its application to polynomial oscillators Perturbation method for non-square Hamiltonians and its application to polynomial oscillators

2005-03-07

arxiv.org/abs/math-ph/0503011v2

Phys. Lett. A 341 (2005) 67 - 80

Physics

Mathematical Physics

21 pages

Scientific paper

10.1016/j.physleta.2005.04.061

A remarkable extension of Rayleigh-Schroedinger perturbation method is found.
Its (N+q) x (N+1) - dimensional Hamiltonians (as emerging, e.g., during
quasi-exact constructions of bound states) are non-square matrices at q > 1.
The role of an eigenvalue is played by an energy/coupling q-plet. In all
orders, its perturbations are defined via a q-dimensional inversion.

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