02-495 Osamu Ogurisu

Generalized boundary conditions of a spin-1/2 particle for the Aharonov-Bohm effect combined with a homogeneous magnetic field (301K, Postscript) Nov 28, 02

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Abstract. Exner et.\ al.\ have derived the most general admissible boundary conditions (MGABC) of the Schr\"odinger operator \(H\) for an idealized Aharonov-Bohm flux interacting the plane at the origin on the background of a homogeneous magnetic field [J.\ Math.\ Phys., \textbf{43}, p2151--2168 (2002)]. In this paper, we derive the MGABC of the Dirac-Weyl operator \(Q\) under the same situation. It is differ from \(H\) that the `standard boundary condition,' \begin{math} \lim_{r\to 0}\Psi(r)=0 \end{math}, gives no self-adjoint extension of \(Q\) and that we can obtain exactly spectra and eigenfunctions of all self-adjoint extensions of \(Q\).

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