Related Experiment Video
Updated: Feb 22, 2026

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
Two-dimensional Dirac particles in a Pöschl-Teller waveguide
R R Hartmann1, M E Portnoi2,3
1Physics Department, De La Salle University, 2401 Taft Avenue, Manila, 0922, Philippines. richard.hartmann@dlsu.edu.ph.
Abstract:
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.
Related Concept Videos
The de Broglie Wavelength
The Quantum-Mechanical Model of an Atom
The Pauli Exclusion Principle
Bewley Lattice Diagram
Standing Waves in a Cavity
The Uncertainty Principle

