Derivatives of the Dirac delta function by explicit construction of sequences

American Journal of Physics

Volumn 71, Issue 5, 2003, Pages 462-468

  Boykin, Timothy B ^a  

^a UNIVERSITY OF ALABAMA IN HUNTSVILLE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038393252     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1557302     Document Type: Article

References (9)

1. M. J. Lighthill, An Introduction to Fourier Analysis and Generalised Functions (Cambridge U.P., New York, 1958), Sees. 1.5, 2.2, 2.3.
2. For a formal presentation of the three-dimensional Dirac delta function using the divergence theorem, see, for example, David J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, Upper Saddle River, NJ, 1999), 3rd ed., Sec. 1.5; and Claude Cohen-Tannoudji, Bernard Diu, and Franck Laloë, Quantum Mechanics (Wiley, New York, 1977), Appendix II. The latter also briefly discuss the electric dipole charge density in a manner similar to our introduction of it in Eq. (27), but do not discuss an explicit sequence for it.
3. For a formal presentation of the three-dimensional Dirac delta function using the divergence theorem, see, for example, David J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, Upper Saddle River, NJ, 1999), 3rd ed., Sec. 1.5; and Claude Cohen-Tannoudji, Bernard Diu, and Franck Laloë, Quantum Mechanics (Wiley, New York, 1977), Appendix II. The latter also briefly discuss the electric dipole charge density in a manner similar to our introduction of it in Eq. (27), but do not discuss an explicit sequence for it.
4. Charles P. Frahm, "Some novel delta function identities," Am. J. Phys. 51, 826-829 (1983).
5. Ricardo Estrada and Ram P. Kanwal, "The appearance of nonclassical terms in the analysis of point source fields," Am. J. Phys. 63, 278 (1995).
6. David J. Griffiths, "Hyperfine splitting in the ground state of hydrogen," Am. J. Phys. 50, 698-703 (1982).
7. J. M. Aguirregabiria, A. Hernández, and M. Rivas, "δ-function converging sequences," Am. J. Phys. 70, 180-185 (2002).
8. Ray Skinner and John A. Weil, "An introduction to generalized functions and their application to static and electromagnetic point dipoles, including hyperfine interactions," Am. J. Phys. 57, 777-791 (1989).
9. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), 2nd ed., pp. 139-145.