dorsal/arxiv
View SchemaEigenvalue bounds for a class of singular potentials in N dimensions
| Authors | Richard L. Hall, Nasser Saad |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9811008 |
| URL | https://arxiv.org/abs/quant-ph/9811008 |
| DOI | 10.1088/0305-4470/32/1/014 |
| Journal | J.Phys.A32:133-138,1999 |
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.
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"abstract": "The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963]\nfor smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to\nN-dimensions. In particular a simple formula is derived which bounds the\neigenvalues for the spiked harmonic oscillator potential V(x) = x^2 +\nlambda/x^alpha, alpha \u003e 0, lambda \u003e 0, and is valid for all discrete\neigenvalues, arbitrary angular momentum ell, and spatial dimension N.",
"arxiv_id": "quant-ph/9811008",
"authors": [
"Richard L. Hall",
"Nasser Saad"
],
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"quant-ph",
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"doi": "10.1088/0305-4470/32/1/014",
"journal_ref": "J.Phys.A32:133-138,1999",
"title": "Eigenvalue bounds for a class of singular potentials in N dimensions",
"url": "https://arxiv.org/abs/quant-ph/9811008"
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