dorsal/arxiv
View SchemaExtension Of Bertrand's Theorem And Factorization Of The Radial Schr\"odinger Equation
| Authors | Zuo-Bing Wu, Jin-Yan Zeng |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9812077 |
| URL | https://arxiv.org/abs/quant-ph/9812077 |
| DOI | 10.1063/1.532568 |
| Journal | J.Math.Phys. 39 (1998) 5253-5259 |
Abstract
The Bertrand's theorem is extended, i.e. closed orbits still may exist for other central potentials than the power law Coulomb potential and isotropic harmonic oscillator. It is shown that for the combined potential $V(r)=W(r)+b/r^2$ ($W(r)=ar^{\nu}$), when (and only when) $W(r)$ is the Coulomb potential or isotropic harmonic oscillator, closed orbits still exist for suitable angular momentum. The correspondence between the closeness of classical orbits and the existence of raising and lowering operators derived from the factorization of the radial Schr\"odinger equation is investigated.
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"abstract": "The Bertrand\u0027s theorem is extended, i.e. closed orbits still may exist for\nother central potentials than the power law Coulomb potential and isotropic\nharmonic oscillator. It is shown that for the combined potential\n$V(r)=W(r)+b/r^2$ ($W(r)=ar^{\\nu}$), when (and only when) $W(r)$ is the Coulomb\npotential or isotropic harmonic oscillator, closed orbits still exist for\nsuitable angular momentum. The correspondence between the closeness of\nclassical orbits and the existence of raising and lowering operators derived\nfrom the factorization of the radial Schr\\\"odinger equation is investigated.",
"arxiv_id": "quant-ph/9812077",
"authors": [
"Zuo-Bing Wu",
"Jin-Yan Zeng"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.532568",
"journal_ref": "J.Math.Phys. 39 (1998) 5253-5259",
"title": "Extension Of Bertrand\u0027s Theorem And Factorization Of The Radial Schr\\\"odinger Equation",
"url": "https://arxiv.org/abs/quant-ph/9812077"
},
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