Tight-binding-like expressions for the continuous-space electromagnetic coupling Hamiltonian

American Journal of Physics

Volumn 69, Issue 7, 2001, Pages 793-798

  Boykin, Timothy B ^a  

^a UNIVERSITY OF ALABAMA IN HUNTSVILLE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035588856     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1344169     Document Type: Article

References (12)

1. Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures in Physics, Vol. III (Addison-Wesley, Reading, MA, 1965), pp. 21-1-21-3.
2. M. Graf and P. Vogl, "Electromagnetic fields and dielectric response in empirical tight-binding theory," Phys. Rev. B 51, 4940-4949 (1995).
3. Timothy B. Boykin, R. Chris Bowen, and Gerhard Klimeck, "Electromagnetic coupling and gauge invariance in the empirical tight-binding method," Phys. Rev. B (in press).
4. Timothy B. Boykin, "Incorporation of incompleteness in the kp perturbation theory," Phys. Rev. B 52, 16317-16320 (1995).
5. Claude Cohen-Tannoudji, Bernard Diu, and Franck Lalöe, Quantum Mechanics, translated by Susan Reid Hemley, Nicole Ostrowsky, and Dan Ostrowsky (Wiley, New York, 1977), pp. 315-328.
6. (α) so that the coordinated r′ are therefore general.
7. (x)|r].
8. M. J. Lighthill, An Introduction to Fourier Analysis and Generalised Functions (Cambridge U.P., New York, 1958). p. 19.
9. (y)).
10. Recall that in the Hamiltonian formulation of classical mechanics as well the vector potential enters the equations of motion with the momentum.
11. Equation (23) holds so long as the spin-orbit Hamiltonian is assumed to have only same-site matrix elements; see Refs. 2 and 3 and references therein for details.
12. Joseph Callaway, Quantum Theory of the Solid State, student ed. (Academic, San Diego, 1974), sec. 6.2.3.