SelfAdjoint Extensions of the Pauli Equation in the Presence of a Magnetic Monopole
Abstract
We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of an abelian magnetic monopole and note that it is not selfadjoint in the lowest two angular momentum modes. We then use von Neumann's theory of selfadjoint extensions to construct a selfadjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. However, consistency with the solutions of the Dirac equation limits the possibilities such that conservation of angular momentum is restored. Because the same effect occurs for a spinless particle with a sufficiently attractive inverse square potential, we also study this system. We use this simpler Hamiltonian to compare the eigenfunctions corresponding to a particular selfadjoint extension with the eigenfunctions satisfying a boundary condition consistent with probability conservation.
 Publication:

Annals of Physics
 Pub Date:
 February 1997
 DOI:
 10.1006/aphy.1996.5638
 arXiv:
 arXiv:quantph/9602013
 Bibcode:
 1997AnPhy.254...11K
 Keywords:

 Quantum Physics;
 High Energy Physics  Theory
 EPrint:
 revised version to be published in Annals of Physics (includes a new section comparing the Pauli case to the Dirac case, as well as other improvements), 17 pages, LaTex (using RevTex)