Self-adjoint Dirac type Hamiltonians in one space dimension with a mass jump

TL;DR

This paper characterizes self-adjoint extensions and spectra of one-dimensional Dirac Hamiltonians with a mass jump, analyzing boundary conditions and transport in heterostructures.

Contribution

It provides a comprehensive analysis of self-adjoint Dirac Hamiltonians with mass jumps, including boundary conditions and spectral properties, extending previous models.

Findings

Identified all self-adjoint extensions for the Hamiltonian with a mass jump.

Analyzed boundary conditions affecting wave function behavior.

Reviewed the case of no mass jump as a special limit.

Abstract

Physical self-adjoint extensions and their spectra of the one-dimensional Dirac type Hamiltonian operator in which both the mass and velocity are constant except for a finite jump at one point of the real axis are correctly found. Different boundary conditions on envelope wave functions are studied, and the limiting case of equal masses (with no mass jump) is reviewed. Transport across one-dimensional heterostructures described by the Dirac equation is considered.