Abstract
We present a systematic approach for the separation of variables for the two-dimensional (2D) Dirac equation in polar coordinates. The three vector potential, which couple to the Dirac spinor via minimal coupling, along with the scalar potential are chosen to have angular dependence which emanate the Dirac equation to complete separation of variables. Exact solutions are obtained for a class of solvable potentials along with their relativistic spinor wavefunctions. Particular attention is paid to the situation where the potentials are confined to a quantum dot region and are of scalar, vector and pseudo-scalar type. The study of a single charged impurity embedded in a 2D Dirac equation in the presence of a uniform magnetic field was treated as a particular case of our general study.
| Original language | English |
|---|---|
| Article number | 1450036 |
| Journal | International Journal of Geometric Methods in Modern Physics |
| Volume | 11 |
| Issue number | 4 |
| DOIs | |
| State | Published - Apr 2014 |
Bibliographical note
Funding Information:The generous support provided by the Saudi Center for Theoretical Physics (SCTP) is highly appreciated by all authors. A. Jellal and H. Bahlouli also acknowledge partial support by King Fahd University of Petroleum and Minerals under project, under the theoretical physics research group project RG1306-1 and RG1306-2. A. Jellal and H. Bahlouli thanks the Deanship of Scientific Research at King Faisal University for funding this research number (140232).
Keywords
- Dirac equation
- factorization
- solvable potentials
- special functions
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)