Academy of Sciences, 25068 Řež, Czech Republic\
    E-mail: [exner@ujf.cas.cz]{} 
- |
    Institut für Angewandte Mathematik\
    Technische Universität Graz\
    Steyrergasse 30, 8010 Graz, Austria\
    E-mail: [holzmann@math.tugraz.at]{}
- |
     Department of Theoretical Physics\
    Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež, Czech Republic\
    E-mail: [lotoreichik@ujf.cas.cz ]{} 
author:
- Jussi Behrndt
- Pavel Exner
- Markus Holzmann
- Vladimir Lotoreichik
title: 'On Dirac operators in with electrostatic and Lorentz scalar -shell interactions'
---

Introduction
============

Working with the equations of motion there is a particular interest to find solutions which are exact and which correspond to specific physical systems. Such an ideal treatment was possible, for instance, in the quantum mechanical explanation of the spectral properties of one-electron atoms. However, such situations are rare and hence, the original model is often replaced by an idealized one which is mathematically accessible and reflects at the same time the physical reality to a reasonable degree. In many problems this can be achieved by using singular potentials supported on sets of measure zero. This method is used highly successfully in nonrelativistic quantum mechanics, cf. the monograph [@AGHH05].

Life becomes more complicated when the systems under consideration are relativistic, described by the Dirac equation. Here there 