Perturbation method for non-square Hamiltonians and its application to polynomial oscillators
arXiv:math-ph/0503011 · doi:10.1016/j.physleta.2005.04.061
Abstract
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.
21 pages