 02495 Osamu Ogurisu
 Generalized boundary conditions of a spin1/2 particle for the AharonovBohm effect combined with a homogeneous magnetic field
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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 AharonovBohm flux interacting the plane at the origin on
the background of a homogeneous magnetic field [J.\ Math.\ Phys.,
\textbf{43}, p21512168 (2002)]. In this paper, we derive the
MGABC of the DiracWeyl 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 selfadjoint extension of \(Q\) and that we can obtain
exactly spectra and eigenfunctions of all selfadjoint extensions of
\(Q\).
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