dorsal/arxiv
View SchemaGroup Approach to the Quantization of the P\"oschl-Teller dynamics
| Authors | V. Aldaya, J. Guerrero |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410009 |
| URL | https://arxiv.org/abs/quant-ph/0410009 |
| DOI | 10.1088/0305-4470/38/31/005 |
Abstract
The quantum dynamics of a particle in the Modified P\"oschl-Teller potential is derived from the group $SL(2,R)$ by applying a Group Approach to Quantization (GAQ). The explicit form of the Hamiltonian as well as the ladder operators is found in the enveloping algebra of this basic symmetry group. The present algorithm provides a physical realization of the non-unitary, finite-dimensional, irreducible representations of the $SL(2,R)$ group. The non-unitarity manifests itself in that only half of the states are normalizable, in contrast with the representations of SU(2) where all the states are physical.
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"abstract": "The quantum dynamics of a particle in the Modified P\\\"oschl-Teller potential\nis derived from the group $SL(2,R)$ by applying a Group Approach to\nQuantization (GAQ). The explicit form of the Hamiltonian as well as the ladder\noperators is found in the enveloping algebra of this basic symmetry group. The\npresent algorithm provides a physical realization of the non-unitary,\nfinite-dimensional, irreducible representations of the $SL(2,R)$ group. The\nnon-unitarity manifests itself in that only half of the states are\nnormalizable, in contrast with the representations of SU(2) where all the\nstates are physical.",
"arxiv_id": "quant-ph/0410009",
"authors": [
"V. Aldaya",
"J. Guerrero"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"physics.chem-ph"
],
"doi": "10.1088/0305-4470/38/31/005",
"title": "Group Approach to the Quantization of the P\\\"oschl-Teller dynamics",
"url": "https://arxiv.org/abs/quant-ph/0410009"
},
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