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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2007 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.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| _version_ | 1862532417995145216 |
|---|---|
| author | Fülöp, T. |
| author_facet | Fülöp, T. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-11-24T04:38:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147221 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:38:57Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fülöp, T. 2019-02-13T19:17:59Z 2019-02-13T19:17:59Z 2007 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 https://nasplib.isofts.kiev.ua/handle/123456789/147221 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. This paper is a contribution to the Proceedings of the 3-rd Microconference “Analytic and Algebraic Methods III”. Work supported in part by the Czech Ministry of Education, Youth and Sports within the project LC06002. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian Article published earlier |
| spellingShingle | Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian Fülöp, T. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147221 |
| work_keys_str_mv | AT fulopt singularpotentialsinquantummechanicsandambiguityintheselfadjointhamiltonian |