Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space

TL;DR

This paper investigates the quantum behavior of a spin-1/2 particle in a conical space with an Aharonov-Bohm potential, addressing the singularity issue via self-adjoint extension, and providing a unified approach for bound and scattering states.

Contribution

It introduces a general method using self-adjoint extension to handle singular Hamiltonians in the Aharonov-Bohm problem within conical space, linking the extension parameter to physical properties.

Findings

Unified self-adjoint extension parameter for bound and scattering states.

Method applicable to any quantum system with singular Hamiltonians.

Clarification of the Zeeman interaction's role in conical space.

Abstract

We examine the bound state and scattering problem of a spin-one-half particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit. The crucial problem of the \delta-function singularity coming from the Zeeman spin interaction with the magnetic flux tube is solved through the self-adjoint extension method. Using two different approaches already known in the literature, both based on the self-adjoint extension method, we obtain the self-adjoint extension parameter to the bound state and scattering scenarios in terms of the physics of the problem. It is shown that such a parameter is the same for both situations. The method is general and is suitable for any quantum system with a singular Hamiltonian that has bound and scattering states.