| Issue |
EPL
Volume 120, Number 3, November 2017
|
|
|---|---|---|
| Article Number | 30006 | |
| Number of page(s) | 7 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/120/30006 | |
| Published online | 23 January 2018 | |
Dirac Green function for δ potentials
1 Departamento de Didáctica de las Ciencias Experimentales, Universidad de Valladolid - 47011 Valladolid, Spain
2 Department of Physics, Clarkson University - Potsdam, NY 13699, USA
3 Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid 47011 Valladolid, Spain
(a) luismiguel.nieto.calzada@uva.es
Received: 20 October 2017
Accepted: 5 January 2018
The Green function for a singular one-dimensional 
potential is explicitly obtained in the relativistic context of the Dirac equation, using Dyson's equation. From it, two bound states are easily found, one for the particle and another for the antiparticle, both depending on the δ potential intensity. When a second δ perturbation is introduced at a different point, the problem can also be solved analytically, for the possible bound states. A transcendental equation is obtained, which can be considered as a relativistic generalization of the well-known Lambert equation.
PACS: 03.65.Pm – Relativistic wave equations / 03.65.Ge – Solutions of wave equations: bound states / 03.65.Db – Functional analytical methods
© EPLA, 2018
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