Eigenvalue bounds for a class of singular potentials in N dimensions

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.