Quantization of exciton in magnetic field background

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.