Perturbation expansions for the spiked harmonic oscillator and related series involving the gamma function
- 28 July 2000
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 33 (31) , 5531-5537
- https://doi.org/10.1088/0305-4470/33/31/308
Abstract
We study weak-coupling perturbation expansions for the ground-state energy of the Hamiltonian with the generalized spiked harmonic oscillator potential V(x) = Bx2 + (A/x2) + (λ/xα), and also for the bottoms of the angular-momentum subspaces labelled by l = 0,1,... , in N dimensions corresponding to the spiked harmonic oscillator potential V(x) = x2 + (λ/xα), where α is a real positive parameter. A method of Znojil (Znojil M 1993 J. Math. Phys. 34 4914) is then applied to obtain closed-form expressions for the sums of some infinite series whose terms involve ratios and products of gamma functions.Keywords
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