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
- URL
- http://stacks.iop.org/0305-4470/36/487/a30213.pdf; http://www.iop.org/;
- PII
- S0305-4470(03)54505-X;
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