dorsal/arxiv
View SchemaGauge transformations for a driven quantum particle in an infinite square well
| Authors | Stefan Weigert |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9811070 |
| URL | https://arxiv.org/abs/quant-ph/9811070 |
| Journal | Found. Phys. 29 (1999) 1785 |
Abstract
Quantum mechanics of a particle in an infinite square well under the influence of a time-dependent electric field is reconsidered. In some gauge, the Hamiltonian depends linearly on the momentum operator which is symmetric but not self-adjoint when defined on a finite interval. In spite of this symmetric part, the Hamiltonian operator is shown to be self-adjoint. This follows from a theorem by Kato and Rellich which guarantees the stability of a self-adjoint operator under certain symmetric perturbations. The result, which has been assumed tacitly by other authors, is important in order to establish the equivalence of different Hamiltonian operators related to each other by quantum gauge transformations. Implications for the quantization procedure of a particle in a box are pointed out.
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"abstract": "Quantum mechanics of a particle in an infinite square well under the\ninfluence of a time-dependent electric field is reconsidered. In some gauge,\nthe Hamiltonian depends linearly on the momentum operator which is symmetric\nbut not self-adjoint when defined on a finite interval. In spite of this\nsymmetric part, the Hamiltonian operator is shown to be self-adjoint. This\nfollows from a theorem by Kato and Rellich which guarantees the stability of a\nself-adjoint operator under certain symmetric perturbations. The result, which\nhas been assumed tacitly by other authors, is important in order to establish\nthe equivalence of different Hamiltonian operators related to each other by\nquantum gauge transformations. Implications for the quantization procedure of a\nparticle in a box are pointed out.",
"arxiv_id": "quant-ph/9811070",
"authors": [
"Stefan Weigert"
],
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"journal_ref": "Found. Phys. 29 (1999) 1785",
"title": "Gauge transformations for a driven quantum particle in an infinite square well",
"url": "https://arxiv.org/abs/quant-ph/9811070"
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