dorsal/arxiv
View SchemaGeneralized Morse Potential: Symmetry and Satellite Potentials
| Authors | A. Del Sol Mesa, C. Quesne, Yu. F. Smirnov |
|---|---|
| Categories | |
| ArXiv ID | physics/9708004 |
| URL | https://arxiv.org/abs/physics/9708004 |
| DOI | 10.1088/0305-4470/31/1/028 |
| Journal | J.Phys.A31:321-335,1998 |
Abstract
We study in detail the bound state spectrum of the generalized Morse potential~(GMP), which was proposed by Deng and Fan as a potential function for diatomic molecules. By connecting the corresponding Schr\"odinger equation with the Laplace equation on the hyperboloid and the Schr\"odinger equation for the P\"oschl-Teller potential, we explain the exact solvability of the problem by an $so(2,2)$ symmetry algebra, and obtain an explicit realization of the latter as $su(1,1) \oplus su(1,1)$. We prove that some of the $so(2,2)$ generators connect among themselves wave functions belonging to different GMP's (called satellite potentials). The conserved quantity is some combination of the potential parameters instead of the level energy, as for potential algebras. Hence, $so(2,2)$ belongs to a new class of symmetry algebras. We also stress the usefulness of our algebraic results for simplifying the calculation of Frank-Condon factors for electromagnetic transitions between rovibrational levels based on different electronic states.
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"abstract": "We study in detail the bound state spectrum of the generalized Morse\npotential~(GMP), which was proposed by Deng and Fan as a potential function for\ndiatomic molecules. By connecting the corresponding Schr\\\"odinger equation with\nthe Laplace equation on the hyperboloid and the Schr\\\"odinger equation for the\nP\\\"oschl-Teller potential, we explain the exact solvability of the problem by\nan $so(2,2)$ symmetry algebra, and obtain an explicit realization of the latter\nas $su(1,1) \\oplus su(1,1)$. We prove that some of the $so(2,2)$ generators\nconnect among themselves wave functions belonging to different GMP\u0027s (called\nsatellite potentials). The conserved quantity is some combination of the\npotential parameters instead of the level energy, as for potential algebras.\nHence, $so(2,2)$ belongs to a new class of symmetry algebras. We also stress\nthe usefulness of our algebraic results for simplifying the calculation of\nFrank-Condon factors for electromagnetic transitions between rovibrational\nlevels based on different electronic states.",
"arxiv_id": "physics/9708004",
"authors": [
"A. Del Sol Mesa",
"C. Quesne",
"Yu. F. Smirnov"
],
"categories": [
"math-ph",
"hep-th",
"math.MP",
"physics.atom-ph"
],
"doi": "10.1088/0305-4470/31/1/028",
"journal_ref": "J.Phys.A31:321-335,1998",
"title": "Generalized Morse Potential: Symmetry and Satellite Potentials",
"url": "https://arxiv.org/abs/physics/9708004"
},
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