Perurbation expansions for the spiked harmonic oscillator and related series involving the gamma function

Details Perurbation expansions for the spiked harmonic oscillator and related series involving the gamma function Perurbation expansions for the spiked harmonic oscillator and related series involving the gamma function

2000-06-27

arxiv.org/abs/math-ph/0006024v1

J. Phys. A 33, 5531-5537 (2000)

Physics

Mathematical Physics

9 pages

Scientific paper

10.1088/0305-4470/33/31/308

We study weak-coupling perturbation expansions for the ground-state energy of the Hamiltonian with the generalized spiked harmonic oscillator potential V(x) = Bx^2 + A/x^2 + lambda/x^alpha, and also for the bottoms of the angular momentum subspaces labelled by ell = 0,1,2 ..., in N-dimensions corresponding to the spiked harmonic oscillator potential: V(x) = x^2 + lambda/x^alpha, where alpha is a real positive parameter. A method of Znojil is then applied to obtain closed form expressions for the sums of some infinite series whose terms involve ratios and products of gamma functions.

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