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

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 
 \(Q\).