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

Richard L. Hall·Nasser Saad
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Abstract

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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Richard L. Hall, Nasser Saad. 2000-06-27. Perurbation expansions for the spiked harmonic oscillator and related series involving the gamma function. https://doi.org/10.1088/0305-4470%2F33%2F31%2F308

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