dorsal/arxiv
View SchemaAnalysis of the SGA method for obtaining energy spectra
| Authors | Patricio Cordero, Jamil Daboul |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503011 |
| URL | https://arxiv.org/abs/quant-ph/0503011 |
Abstract
We analyze and clarify how the SGA (spectrum generating algebra) method has been applied to different potentials. We emphasize that each energy level $E_\nu$ obtained originally by Morse belongs to a {\em different} ${\mathfrak {so}}(2,1)$ multiplet. The corresponding wavefunctions $\Psi_\nu$ are eigenfuntions of the compact generators $J^\nu_0$ with the same eigenvalue $k_0$, but with different eigenvalues $q_\nu$ of the Casimir operators $Q$. We derive a general expression for all effective potentials which have $\Psi_{\lambda_\nu,\nu+m}(r) \propto (J_+^\nu)^m ~\Psi_{\lambda_\nu,\nu}(r)$ as eigenfunctions, without using super-symmetry formalism. The different actions of SGA is further illustrated by two diagrams.
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"abstract": "We analyze and clarify how the SGA (spectrum generating algebra) method has\nbeen applied to different potentials. We emphasize that each energy level\n$E_\\nu$ obtained originally by Morse belongs to a {\\em different} ${\\mathfrak\n{so}}(2,1)$ multiplet. The corresponding wavefunctions $\\Psi_\\nu$ are\neigenfuntions of the compact generators $J^\\nu_0$ with the same eigenvalue\n$k_0$, but with different eigenvalues $q_\\nu$ of the Casimir operators $Q$. We\nderive a general expression for all effective potentials which have\n$\\Psi_{\\lambda_\\nu,\\nu+m}(r) \\propto (J_+^\\nu)^m ~\\Psi_{\\lambda_\\nu,\\nu}(r)$ as\neigenfunctions, without using super-symmetry formalism. The different actions\nof SGA is further illustrated by two diagrams.",
"arxiv_id": "quant-ph/0503011",
"authors": [
"Patricio Cordero",
"Jamil Daboul"
],
"categories": [
"quant-ph"
],
"title": "Analysis of the SGA method for obtaining energy spectra",
"url": "https://arxiv.org/abs/quant-ph/0503011"
},
"schema_id": "dorsal/arxiv",
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"execution_id": "3e6bc78a-c12d-4164-b46b-def25e6f006d",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
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