Published January 17, 2003 | Version v1
Journal article

Energy bounds for a class of singular potentials and some related series

  • 1. Department of Mathematics and Computer Science, University of Prince Edward Island, 550 University Avenue, Charlottetown (Canada)
  • 2. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, PQ(Canada)
  • 3. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, PQ (Canada)

Description

Perturbation expansions up to third order for the generalized spiked harmonic oscillator Hamiltonians H = -d2/dx2 + x2 + A/x2 + λ/xα(A ≥ 0, 2γ > α, γ = 1 + 1/2√1 + 4A) and small values of the coupling λ > 0, are developed. Upper and lower bounds for the eigenvalues are computed by the procedure of Burrows et al (1987 J. Phys. A: Math. Gen. 20 889-97) for assessing the accuracy of a truncated perturbation expansion. Closed-form sums for some related perturbation double infinite series then immediately follow as a result of this investigation

Availability note (English)

Available online at http://stacks.iop.org/0305-4470/36/487/a30213.pdf or at the Web site for the Journal of Physics. A, Mathematical and General (ISSN 1361-6447) http://www.iop.org/

Additional details

Identifiers

Publishing Information

Journal Title
Journal of Physics. A, Mathematical and General
Journal Volume
36
Journal Issue
2
Journal Page Range
p. 487-498
ISSN
0305-4470
CODEN
JPHAC5

INIS

Country of Publication
United Kingdom
Country of Input or Organization
International Atomic Energy Agency (IAEA)
INIS RN
34020169
Subject category
S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
Descriptors DEI
EIGENVALUES; HAMILTONIANS; HARMONIC OSCILLATOR MODELS; PERTURBATION THEORY; POTENTIALS
Descriptors DEC
MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; QUANTUM OPERATORS