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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.

Keywords

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

R2 v1 2026-07-22T16:23:25.298Z