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...
Збережено в:
Видавець: | Інститут математики НАН України |
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Дата: | 2007 |
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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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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of UkraineРезюме: | 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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