Two-dimensional Dirac particles in a Pöschl-Teller waveguide

• Main Authors: Hartmann, R. R., Portnoi, M. E.
• Format: text
• Published: Animo Repository 2017
• Subjects: Wave guides; Dirac equation; Physics
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/366
• Institution: De La Salle University

© 2017 The Author(s). We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional Pöschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while the eigenvalues are determined via the solutions of a simple transcendental equation. For the symmetric case, the eigenfunctions of the supercritical states are expressed as spheroidal wave functions, and approximate analytical expressions are obtained for the corresponding eigenvalues. A universal condition for any square integrable symmetric potential is obtained for the minimum strength of the potential required to hold a bound state of zero energy. Applications for smooth electron waveguides in 2D Dirac-Weyl systems are discussed.