About this Journal Submit a Manuscript Table of Contents
Journal of Atomic, Molecular, and Optical Physics
Volume 2011 (2011), Article ID 573179, 4 pages
http://dx.doi.org/10.1155/2011/573179
Research Article

Bound States in Delta Function Potentials

Department of Physics, University of Colorado, Boulder, CO 80309, USA

Received 28 June 2011; Accepted 18 September 2011

Academic Editor: Gregory Lapicki

Copyright © 2011 Sydney Geltman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, 3rd edition, 1940.
  2. L. H. Thomas, “The interaction between a neutron and a proton and the structure of H3,” Physical Review, vol. 47, no. 12, pp. 903–909, 1935. View at Publisher · View at Google Scholar · View at Scopus
  3. S. Geltman, “Ionization of a model atom by a pulse of coherent radiation,” Journal of Physics B, vol. 10, no. 5, article 019, pp. 831–840, 1977. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Geltman, “Short-pulse model-atom studies of ionization in intense laser fields,” Journal of Physics B, vol. 27, p. 1497, 1994.
  5. J. Z. Kamiński, “Stabilization and the zero-range models,” Physical Review A, vol. 52, no. 6, pp. 4976–4979, 1995. View at Publisher · View at Google Scholar
  6. Q. Su, B. P. Irving, C. W. Johnson, and J. H. Eberly, “Stabilization of a one-dimensional short-range model atom in intense laser fields,” Journal of Physics B, vol. 29, no. 23, pp. 5755–5764, 1996. View at Scopus
  7. S. Geltman, “Comment on “stabilization of a one-dimensional short-range model atom in intense laser fields”,” Journal of Physics B, vol. 32, no. 3, pp. 853–856, 1999. View at Scopus
  8. E. P. Gross, “Structure of a quantized vortex in boson systems,” Nuovo Cimento, vol. 20, no. 3, pp. 454–477, 1961. View at Publisher · View at Google Scholar · View at Scopus
  9. E. P. Gross, “Hydrodynamics of a superfluid condensate,” Journal of Mathematical Physics, vol. 4, no. 2, pp. 195–207, 1963.
  10. L. P. Pitaevskii, “Vortex lines in an imperfect Bose gas,” Soviet Physics—JETP, vol. 13, p. 451, 1961.
  11. S. Geltman, “A critique on the misuse of the Gross-Pitaevskii equation,” EPL, vol. 87, no. 1, p. 13001, 2009. View at Publisher · View at Google Scholar
  12. A. Farrell and B. P. van Zyl, “S-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions,” Canadian Journal of Physics, vol. 88, no. 11, pp. 817–824, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. M. M. Nieto, “Existence of bound states in continuous 0 < D < ∞ dimensions,” Physics Letters, Section A, vol. 293, no. 1-2, pp. 10–16, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. M. Abramowitz, I. A. Stegun, et al., Handbook of Mathematical Functions, U S Government Printing Office, 1964.
  15. E. Fermi, Ric. Sci., vol. 7, p. 13, 1936.
  16. N. Levinsonson, Det kongelige Danske Videnskabernes Selskab Matematisk-Fysiske Meddelelser, vol. 25, no. 9, 1949.
  17. K. Wodkiewicz, “Fermi pseudopotential in arbitrary dimensions,” Physical Review A, vol. 43, p. 68, 1991.
  18. R. Jackiw, Beg Memorial Volume, World Scientific, 1991.
  19. A. Cabo, J. L. Lucio, and H. Mercado, “On scale invariance and anomalies in quantum mechanics,” American Journal of Physics, vol. 66, no. 3, pp. 240–246, 1998.
  20. I. Mitra, A. DasGupta, and B. Dutta-Roy, “Regularization and renormalization in scattering from Dirac delta potentials,” American Journal of Physics, vol. 66, no. 12, pp. 1101–1109, 1998.
  21. S.-L. Neyo, “Regularization methods for delta-function potential in two-dimensional quantum mechanics,” American Journal of Physics, vol. 68, p. 571, 2000.
  22. P. Gosdzinsky and R. Tarrach, “Learning quantum field theory from elementary quantum mechanics,” American Journal of Physics, vol. 59, p. 70, 1991.