Quantum Mechanics of an Electron in a Homogeneous Magnetic Field and a Singular Magnetic Flux Tube

✍ Scribed by Hans-Peter Thienel

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 246 KB
• Volume: 280
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1999.5985

✦ Synopsis

The eigenvalue problem of the Hamiltonian of an electron confined to a plane and subjected to a perpendicular time-independent magnetic field which is the sum of a homogeneous field and an additional field contributed by a singular flux tube, i.e., of zero width, is investigated. Since both a direct approach based on distribution-valued operators and a limit process starting from a non-singular flux tube, i.e., of finite size, fail, an alternative method is applied leading to consistent results. An essential feature is quantum mechanical supersymmetry at g=2 which imposes, by proper representation, the correct choice of ``boundary conditions.'' The corresponding representation of the Hilbert space in coordinate space differs from the usual space of square-integrable 2-spinors, entailing other unusual properties. The analysis is extended to g{2 so that supersymmetry is explicitly broken. Finally, the singular Aharonov Bohm system with the same amount of singular flux is analyzed by making use of the fact that the Hilbert space must be the same.