Energy bounds for the spinless Salpeter equation: harmonic oscillator

Authors
Hall, RL Lucha, W Schoberl, FF
Citation
Rl. Hall et al., Energy bounds for the spinless Salpeter equation: harmonic oscillator, J PHYS A, 34(24), 2001, pp. 5059-5063
Citations number
12
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
34
Issue
24
Year of publication
2001
Pages
5059 - 5063
Database
ISI
SICI code
0305-4470(20010622)34:24<5059:EBFTSS>2.0.ZU;2-E
Abstract
We study the eigenvalues epsilon (nl) of the Salpeter Hamiltonian H = beta rootm(2) + p(2) + vr(2), v > 0, beta > 0, in three dimensions. By using geo metrical arguments we show that, for suitable values of P, here provided, t he simple semiclassical formula [GRAPHICS] provides both upper and lower energy bounds for all the eigenvalues of the problem.