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

2005/03/31 by Miloslav Znojil
Mathematics · Physics and Astronomy · #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP #msc:15A90 #msc:34L16 #msc:34M25 #msc:65F15 #msc:81Q05

paper · pdf · doi:10.1016/j.physleta.2005.04.061

published as Phys. Lett. A 341 (2005) 67 - 80 · 21 pages

arxiv created 2005/04/25 · openalex publication_date 2005/05/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Hamiltonian and linear-space structure for damped oscillators: II. Critical points
• Hamiltonian and linear-space structure for damped oscillators: I. General theory

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