Dirac deltas and discontinuous functions

American Journal of Physics

Volumn 67, Issue 5, 1999, Pages 446-447

  Griffiths, David ^a   Walborn, Stephen ^a  

^a REED COLLEGE   (United States)

Author keywords

02; 03.65

Indexed keywords

EID: 85019466963     PISSN: 00029505     EISSN: 19432909     Source Type: Journal    
DOI: 10.1119/1.19283     Document Type: Letter

References (10)

1. See, for example, B. Sutherland and D. C. Mattis, “Ambiguities with the relativistic δ-function potential,” Phys. Rev. A PLRAAN 24, 1194 (1981)
2. B. H. J. McKellar and G. J. Stephenson, Jr., “Relativistic quarks in one-dimensional periodic structures,” Phys. Rev. C PRYCAN 35, 2262–2271 (1987)
3. M. G. Calkin, D. Kiang, and Y. Nogami, “Proper treatment of the delta function potential in the one-dimensional Dirac equation,” Am. J. Phys. AJPIAS 55, 737–739 (1987)
4. C. L. Roy, “Boundary conditions across a δ-function potential in the one-dimensional Dirac equation,” Phys. Rev. A PLRAAN 47, 3417–3419 (1993)
5. F. A. B. Coutinho, Y. Nogami, and J. F. Perez, “Generalized point interactions in one-dimensional quantum mechanics,” J. Phys. A JPHAC5 30, 3937–3945 (1997).
6. See, for example, I. R. Lapidus, “Relativistic one-dimensional hydrogen atom,” Am. J. Phys. AJPIAS 51, 1036–1038 (1983), corrected by M. G. Calkin, D. Kiang, and Y. Nogami, “Proper treatment of the delta function potential in the one-dimensional Dirac equation,” Am. J. Phys. AJPIAS 55, 731–739 (1987)
7. T. H. Solomon and S. Fallieros, “Relativistic One-dimensional Binding and Two-dimensional Motion,” J. Franklin Inst. JFINAB 320, 323–344 (1985)
8. D. J. Griffiths, “Boundary conditions at the derivative of a delta function,” J. Phys. A JPHAC5 26, 2265–2267 (1993), corrected by F. A. B. Coutinho, Y. Nogami, and J. F. Perez, “Generalized point interactions in one-dimensional quantum mechanics,” J. Phys. A JPHAC5 30, 3937–3945 (1997). and by G. Barton and D. Waxman, “Wave Equations with Point-Support Potentials Having Dimensionless Strength Parameters,” Sussex report 1994 (unpublished)
9. M. A. Maize and C. A. Burkholder, “Electric polarizability and the solution of an inhomogeneous differential equation,” Am. J. Phys. AJPIAS 63, 244–247 (1995), corrected by F. A. B. Coutinho, Y. Nogami, and F. M. Toyama, “Logarithmic perturbation expansion for the Dirac equation in one dimension: Application to the polarizability calculation,” Am. J. Phys. 65, 788–794 (1997)
10. M. A. Maize, S. Paulson, and A. D’Avanti, “Electric polarizability of a relativistic particle,” Am. J. Phys. 65, 888–892 (1997).