Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian
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| Creator |
Fülöp, T.
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| Description |
For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and V(x) = g/x² with the coefficient g in a certain range (x being a space coordinate in one or more dimensions), the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the self-adjoint version chosen. The article discusses how the self-adjoint domains can be identified in terms of a boundary condition for the asymptotic behaviour of the wave functions around the singularity, and what physical differences emerge for different self-adjoint versions of the Hamiltonian. The paper reviews and interprets known results, with the intention to provide a practical guide for all those interested in how to approach these ambiguous situations.
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| Date |
2019-02-13T19:17:59Z
2019-02-13T19:17:59Z 2007 |
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| Type |
Article
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| Identifier |
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian / T. Fülöp // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 22 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 81Q10 http://dspace.nbuv.gov.ua/handle/123456789/147221 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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