Perturbation expansions for a class of singular potentials

Details Perturbation expansions for a class of singular potentials Perturbation expansions for a class of singular potentials

2003-09-30

arxiv.org/abs/math-ph/0309067v1

J. Math. Phys. 44, 5021-5041 (2003)

Physics

Mathematical Physics

23 pages

Scientific paper

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.

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