Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2007
• ISSN: 1815-0659
• Main Author: Fülöp, T.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147221
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...