Discrete spectrum of stationary Dirac operator in a square-well potential

Autor: Samantha Ana Cristina Loredo Ramírez
Coautor(es): Dr. Víctor Barrera Figueroa. Dr. Vladimir Rabinovich Likhtman.
This work addresses the analysis of stationary Dirac operator of the relativistic quantum mechanics for the study of potential wells. From a mathematical point of view, this operator has not been extensively studied yet because there is still an unambiguous quantum mechanical interpretation. For this reason, we calculate the general solution of the Dirac system, the dispersion relation and we study the behavior of this system with a piecewise potential. In addition, we review the SPPS (Spectral Parameter Power Series) method to construct a representation for solutions of the one-dimensional Dirac system.