Numerical analysis of one-dimensional Dirac equation with singular potentials

Ponente(s): Samantha Ana Cristina Loredo Ramírez, Dr. Víctor Barrera Figueroa Dr. Vladimir Rabinovich Likhtman
This work is dedicated to the study of the discrete spectrum and the construction of the eigenfunctions of the Dirac equation with regular and singular potentials in terms of power series of the spectral parameter [1]. In particular, this topic addresses the analysis of the spectral properties of one-dimensional stationary Dirac equation that is important in relativistic quantum mechanics for massive 1/2-spin particles. The Spectral Parameter Power Series method [2] lead us an analytic expression to determine the characteristic equation that is given by the Taylor series of an analytic function. Based on the results of this study the numerical implementation follows in some examples. References [1] Gutiérrez J N and Torba S M. Appl Math Comput 370 (2020). [2] Kravchenko V V and Porter R M. Math Method App Sci 33 (2010) 459.