dorsal/arxiv
View SchemaVariational analysis for a generalized spiked harmonic oscillator
| Authors | Richard L. Hall, Nasser Saad |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9911118 |
| URL | https://arxiv.org/abs/quant-ph/9911118 |
| DOI | 10.1088/0305-4470/33/3/310 |
| Journal | J. Phys. A 33, 569-578 (2000) |
Abstract
A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.
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"abstract": "A variational analysis is presented for the generalized spiked harmonic\noscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 +\nlambda/x^alpha, and alpha and lambda are real positive parameters. The\nformalism makes use of a basis provided by exact solutions of Schroedinger\u0027s\nequation for the Gol\u0027dman and Krivchenkov Hamiltonian (alpha = 2), and the\ncorresponding matrix elements that were previously found. For all the discrete\neigenvalues the method provides bounds which improve as the dimension of the\nbasis set is increased. Extension to the N-dimensional case in arbitrary\nangular-momentum subspaces is also presented. By minimizing over the free\nparameter A, we are able to reduce substantially the number of basis functions\nneeded for a given accuracy.",
"arxiv_id": "quant-ph/9911118",
"authors": [
"Richard L. Hall",
"Nasser Saad"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"doi": "10.1088/0305-4470/33/3/310",
"journal_ref": "J. Phys. A 33, 569-578 (2000)",
"title": "Variational analysis for a generalized spiked harmonic oscillator",
"url": "https://arxiv.org/abs/quant-ph/9911118"
},
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