Eigenvalue bounds for a class of singular potentials in N dimensions
Quantum Physics
2008-11-26 v1 Mathematical Physics
math.MP
Abstract
The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963] for smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to N-dimensions. In particular a simple formula is derived which bounds the eigenvalues for the spiked harmonic oscillator potential V(x) = x^2 + lambda/x^alpha, alpha > 0, lambda > 0, and is valid for all discrete eigenvalues, arbitrary angular momentum ell, and spatial dimension N.
Cite
@article{arxiv.quant-ph/9811008,
title = {Eigenvalue bounds for a class of singular potentials in N dimensions},
author = {Richard L. Hall and Nasser Saad},
journal= {arXiv preprint arXiv:quant-ph/9811008},
year = {2008}
}
Comments
10 pages (plain tex with 2 ps figures). J.Phys.A:Math.Gen.(In Press)