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Эта публикация цитируется в 27 научных статьях (всего в 27 статьях)
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian
Tamáas Fülöp Montavid Research Group, Budapest, Soroksári út 38-40, 1095, Hungary
Аннотация:
For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and $V(x)=g/x^2$ 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.
Ключевые слова:
quantum mechanics; singular potential; self-adjointness; boundary condition.
Поступила: 7 августа 2007 г.; в окончательном варианте 8 ноября 2007 г.; опубликована 16 ноября 2007 г.
Образец цитирования:
Tamáas Fülöp, “Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian”, SIGMA, 3 (2007), 107, 12 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma233 https://www.mathnet.ru/rus/sigma/v3/p107
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