Eigenvalue bounds for a class of singular potentials in N dimensions

Details Eigenvalue bounds for a class of singular potentials in N dimensions Eigenvalue bounds for a class of singular potentials in N dimensions

1998-11-03

arxiv.org/abs/quant-ph/9811008v1

J.Phys.A32:133-138,1999

Physics

Quantum Physics

10 pages (plain tex with 2 ps figures). J.Phys.A:Math.Gen.(In Press)

Scientific paper

10.1088/0305-4470/32/1/014

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.

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