ua nt - p h / 96 02 01 3 v 1 1 8 Fe b 19 96 Self - Adjoint Extensions of the Pauli Equation in the Presence of a Magnetic Monopole
نویسندگان
چکیده
We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of a 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. 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.
منابع مشابه
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