Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian
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...
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| Дата: | 2007 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147221 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1472212019-02-14T01:26:55Z Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian Fülöp, T. 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. 2007 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Fülöp, T. |
| spellingShingle |
Fülöp, T. Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Fülöp, T. |
| author_sort |
Fülöp, T. |
| title |
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian |
| title_short |
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian |
| title_full |
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian |
| title_fullStr |
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian |
| title_full_unstemmed |
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian |
| title_sort |
singular potentials in quantum mechanics and ambiguity in the self-adjoint hamiltonian |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147221 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT fulopt singularpotentialsinquantummechanicsandambiguityintheselfadjointhamiltonian |
| first_indexed |
2023-05-20T17:27:00Z |
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2023-05-20T17:27:00Z |
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1796153320312668160 |