Physics – Quantum Physics
Scientific paper
1996-02-18
Annals Phys. 254 (1997) 11-24
Physics
Quantum Physics
revised version to be published in Annals of Physics (includes a new section comparing the Pauli case to the Dirac case, as we
Scientific paper
10.1006/aphy.1996.5638
We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of an abelian magnetic monopole and note that it is not self-adjoint in the lowest two angular momentum modes. We then use von Neumann's theory of self-adjoint extensions to construct a self-adjoint 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 self-adjoint extension with the eigenfunctions satisfying a boundary condition consistent with probability conservation.
Karat Edwin R.
Schulz Michael B.
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