OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 1, Iss. 2 — Apr. 1, 1984
  • pp: 169–175

Discretization in the quasi-continuum

Ronald S. Burkey and C. D. Cantrell  »View Author Affiliations

JOSA B, Vol. 1, Issue 2, pp. 169-175 (1984)

View Full Text Article

Enhanced HTML    Acrobat PDF (942 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Straightforward discretization of the equations of motion of a quasi-continuum interacting with an electromagnetic field often leads to physical and numerical difficulties. We derive two distinct methods for reducing the number of energy levels that must be treated explicitly in such calculations. One of these applies to bands of quasi-continua with slowly decreasing shoulders; the other, to bands with rapidly decreasing shoulders.

© 1984 Optical Society of America

Ronald S. Burkey and C. D. Cantrell, "Discretization in the quasi-continuum," J. Opt. Soc. Am. B 1, 169-175 (1984)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. B. W. Shore, "Coherence in the quasi-continuum model," Chem. Phys. Lett. 99, 240–243 (1983). [CrossRef]
  2. J. H. Wilkinson, The Algebraic Eigenvalue Problem (Oxford U. Press, Oxford, 1965); E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge U. Press, Cambridge, 1935), pp. 40–41.
  3. A. A. Makarov, V. T. Platonenko, and V. V. Tyakht, "Interaction of a 'level-band' quantum system with a quasiresonant monochromatic field," Zh. Eksp. Teor. Fiz. 75, 2075–2091 (1978) [Sov. Phys. JETP 48, 1044–1051 (1978)].
  4. J. J. Yeh, C. M. Bowden, and J. H. Eberly, "Interrupted coarsegrained theory of'unimolecular relaxation and stimulated recurrences in photo-excitation of a quasi-continuum," J. Chem. Phys. 76, 5936–5946 (1982); see also J. H. Eberly, J. J. Yeh, and C. M. Bowden, "Interrupted coarse-grained theory of quasicontinuum photo-excitation," Chem. Phys. Lett. 86, 76–80 (1982). [CrossRef]
  5. G. C. Stey and R. W. Gibberd, "Decay of quantum states in some exactly soluble models," Physica 60, 1–26 (1972). [CrossRef]
  6. P. W. Milonni, J. R. Ackerhalt, H. W. Galbraith, and M. L. Shih, "Exponential decay, recurrences, and quantum-mechanical spreading in a quasi-continuum model," Phys. Rev. A 28, 32–39 (1983); R. Lefebvre and J. Savolainen, "Memory functions and recurrences in intramolecular processes," J. Chem. Phys. 60, 2509–2555 (1974). [CrossRef]
  7. C. D. Cantrell, V. S. Letokhov, and A. A. Makarov, "Coherent excitation of multilevel systems by laser light" in Coherent Nonlinear Optics: Recent Advances, M. S. Feld and V. S. Letokhov, eds. (Springer-Verlag, Berlin, 1980). [CrossRef]
  8. G. L. Peterson, C. D. Cantrell, and R. S. Burkey, "Adiabatic excitation of multilevel band systems," Opt. Commun. 43, 123–127 (1982). [CrossRef]
  9. N. M. Witriol, A. J. Galli, W. H. Brumage, and C. M. Bowden, "Criteria for the reduction of the effective manifold of states in models of laser-induced dissociation and chemistry," Opt. Lett. 5, 24–26 (1980). [CrossRef] [PubMed]
  10. R. S. Burkey and C. D. Cantrell, "Solution of the Schrödinger equation for systems driven by an exponential or a semiexponential pulse," Opt. Commun. 43, 64–68 (1982). [CrossRef]
  11. U. W. Hochstrasser, "Orthogonal polynomials" in Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, eds. (U.S. Government Printing Office, Washington, D.C., 1964), p. 773.
  12. D. Jackson, Fourier Series and Orthogonal Polynomials (Collegiate, Menasha, Wise, 1941), Chap. 7.
  13. R. W. Hamming, Numerical Methods for Scientists and Engineers (McGraw-Hill, New York 1962), pp. 118–164.
  14. R. Haydock, "The recursive solution of the Schrödinger equation," Comput. Phys. Commun. 20, 11–16 (1980); R. Haydock, "The recursive solution of the Schrödinger equation," in Solid State Physics, H. Ehrenreich, F. Seitz, and D. Turnbull, eds. (Academic, New York, 1980), Vol. 35, p. 215. [CrossRef]
  15. Z. Bialynicka-Birula, I. Bialynicka-Birula, J. H. Eberly, and B. W. Shore, "Coherent dynamics of N-level atoms and molecules. II. Analytic solutions," Phys. Rev. A 16, 2048–2051 (1977). [CrossRef]
  16. N. M. Witriol, "Including the continuum in the N-level molecule model," Chem. Phys. Lett. 98, 77–80 (1983). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited