Perturbation expansions for a class of singular potentials
Mathematical Physics
2015-06-26 v1 math.MP
Abstract
Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.
Cite
@article{arxiv.math-ph/0309067,
title = {Perturbation expansions for a class of singular potentials},
author = {Nasser Saad and Richard L. Hall and Attila B. von Keviczky},
journal= {arXiv preprint arXiv:math-ph/0309067},
year = {2015}
}
Comments
23 pages