Perturbation expansions for the spiked harmonic oscillator and related series involving the gamma function
نویسندگان
چکیده
We study weak-coupling perturbation expansions for the ground-state energy of the Hamiltonian with the generalized spiked harmonic oscillator potential V (x) = Bx + A x + λ x , 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) = x + λ x , where α 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. PACS 03.65.Ge Perturbation expansions for the spiked harmonic oscillator . . . page 2
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