Singular perturbation potentials

A complete variational treatment is provided for a family of spiked-harmonicA compact topological proof is presented that the set S = {ψ n } of known exact solutions for α = 2 constitutes an orthonormal basis of the Hilbert space L 2 (0, ∞) .Closed-form expressions are derived for the matrix elements of H with respect to S . These analytical results, and the inclusion of a further free parameter, facilitate optimized variational estimation of the eigenvalues of H to high accuracy.PACS 03.65.Ge Spiked harmonic oscillators . . .

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“…We therefore may replace A in Eq. (3.6) with 1) and obtain thereby an exact solutions of N -dimensional radial Schrödinger equation…”

Section: The N -Dimensional Casementioning

confidence: 99%

Spiked harmonic oscillators

Hall

Saad

Keviczky

2002

Journal of Mathematical Physics

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“…This is a detailed extension of Harrell's modified perturbation theory 1 for the class of singular potentials 1) defined on suitable domains in the Hilbert space L 2 (0, ∞) with solutions satisfying Dirichlet boundary conditions. By 'singular' we mean that the familiar RayleighSchrödinger series either do not exist or do not converge.…”

Section: Introductionmentioning

confidence: 99%

Perturbation expansions for a class of singular potentials

Saad

Hall

Keviczky

2003

Journal of Mathematical Physics

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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, known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling λ > 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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“…It is an interesting model not only because of being a singular potential representing a repulsive core in realistic interactions, but also because of its intrinsic properties in view of mathematical physics [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%