dorsal/arxiv
View SchemaStar-quantization of an infinite wall
| Authors | Sergei Kryukov, Mark A. Walton |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508005 |
| URL | https://arxiv.org/abs/quant-ph/0508005 |
| DOI | 10.1139/P06-017 |
| Journal | Can. J. Phys.84:557-563, 2006 |
Abstract
In deformation quantization (a.k.a. the Wigner-Weyl-Moyal formulation of quantum mechanics), we consider a single quantum particle moving freely in one dimension, except for the presence of one infinite potential wall. Dias and Prata pointed out that, surprisingly, its stationary-state Wigner function does not obey the naive equation of motion, i.e. the naive stargenvalue (*-genvalue) equation. We review our recent work on this problem, that treats the infinite wall as the limit of a Liouville potential. Also included are some new results: (i) we show explicitly that the Wigner-Weyl transform of the usual density matrix is the physical solution, (ii) we prove that an effective-mass treatment of the problem is equivalent to the Liouville one, and (iii) we point out that self-adjointness of the operator Hamiltonian requires a boundary potential, but one different from that proposed by Dias and Prata.
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"abstract": "In deformation quantization (a.k.a. the Wigner-Weyl-Moyal formulation of\nquantum mechanics), we consider a single quantum particle moving freely in one\ndimension, except for the presence of one infinite potential wall. Dias and\nPrata pointed out that, surprisingly, its stationary-state Wigner function does\nnot obey the naive equation of motion, i.e. the naive stargenvalue (*-genvalue)\nequation. We review our recent work on this problem, that treats the infinite\nwall as the limit of a Liouville potential. Also included are some new results:\n(i) we show explicitly that the Wigner-Weyl transform of the usual density\nmatrix is the physical solution, (ii) we prove that an effective-mass treatment\nof the problem is equivalent to the Liouville one, and (iii) we point out that\nself-adjointness of the operator Hamiltonian requires a boundary potential, but\none different from that proposed by Dias and Prata.",
"arxiv_id": "quant-ph/0508005",
"authors": [
"Sergei Kryukov",
"Mark A. Walton"
],
"categories": [
"quant-ph"
],
"doi": "10.1139/P06-017",
"journal_ref": "Can. J. Phys.84:557-563, 2006",
"title": "Star-quantization of an infinite wall",
"url": "https://arxiv.org/abs/quant-ph/0508005"
},
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