On the Hermitian of Hamiltonians of Radial Equations

Abstract：

The Hamiltonian of a radial equation is defined on a half-line, and there is an intimate relation between its hermitian and the boundary conditions of the wave functions at the origin. If the wave functions are nonvanishing and convergent at the origin, the Hamiltonian has a one-parameter family of self-adjoint extensions which are related to the condition for the vanishing radial probability current at the origin. In this paper the problem on the hermitian of the Hamiltonian of a radial equation is studied systematically. Some methods for determining the parameter for the fermion moving in a magnetic monopole field are discussed.