Quantization of exciton in magnetic field background

TL;DR

This paper explores a novel approach to modeling excitons in magnetic fields by applying von Neumann's self-adjoint extension method, aiming to better match theoretical predictions with experimental absorption data.

Contribution

It introduces a new quantization scheme for excitons in magnetic fields using self-adjoint extensions, allowing adjustable boundary conditions to improve experimental agreement.

Findings

Bound and scattering state solutions depend on the extension parameter 

The parameter  can be tuned to match experimental absorption spectra

The method provides a flexible framework for exciton modeling in magnetic fields

Abstract

The possible mismatch between the theoretical and experimental absorption of the edge peaks in semiconductors in a magnetic field background may arise due to the approximation scheme used to analytically calculate the absorption coefficient. As a possible remedy we suggest to consider nontrivial boundary conditions on x-y plane by in-equivalently quantizing the exciton in background magnetic field. This inequivalent quantization is based on von Neumann's method of self-adjoint extension, which is characterized by a parameter \Sigma. We obtain bound state solution and scattering state solution, which in general depend upon the self-adjoint extension parameter \Sigma. The parameter \Sigma can be used to fine tune the optical absorption coefficient K(\Sigma) to match with the experiment.