Self-Adjointness of Generalized MIC-Kepler System

TL;DR

This paper investigates the mathematical property of self-adjointness in the generalized MIC-Kepler Hamiltonian, revealing conditions under which the system admits self-adjoint extensions, crucial for quantum physical consistency.

Contribution

It provides a detailed analysis of self-adjoint extensions of the generalized MIC-Kepler Hamiltonian for specific angular momentum values, expanding understanding of its mathematical structure.

Findings

For =0, the system admits a 1-parameter family of self-adjoint extensions.

For  eq 0 but  < 1/2, the system also admits a 1-parameter family of self-adjoint extensions.

Abstract

We have studied the self-adjointness of generalized MIC-Kepler Hamiltonian, obtained from the formally self-adjoint generalized MIC-Kepler Hamiltonian. We have shown that for \tilde l=0, the system admits a 1-parameter family of self-adjoint extensions and for \tilde l \neq 0 but \tilde l <{1/2}, it has also a 1-parameter family of self-adjoint extensions.