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Exact Solutions for Superlattices and How to Recognize them with Computer Algebra

  • Gene Cooperman
  • Lionel Friedman
  • Walter Bloss

Abstract

The study of superlattices has been motivated by the possibility of “custom-engineering” new solid state materials. Using the Kronig-Penney equations for superlattices, we found a novel series expansion solution for several of its physical properties. We derived the first two terms by hand, providing an accurate estimate of the physical quantities of interest. With the aid of MACSYMA, we were later encouraged to derive still higher order terms. To our surprise, the higher order terms reduced to zero for a physically important special case. This motivated further analysis, in which we were able to show our original two-term solution to be an exact, closed form solution in this special case.

Keywords

High Order Term Computer Algebra Schrodinger Equation Apply Physic Letter Important Special Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Dohler, Gottfried, “Solid-State Superlattices,” Scientific American, 249(5), pp. 144–151, Nov., 1983.CrossRefGoogle Scholar
  2. 2.
    W.L. Bloss and L. Friedman, Applied Physics Letters, Vol. 41(11), p. 1023, 1982.CrossRefGoogle Scholar
  3. 3.
    G. Cooperman, L. Friedman, and W.L. Bloss, “Corrections to Enhanced Optical Nonlinearity of Superlattices,” Applied Physics Letters, Vol. 44(10), pp. 977–979, May 15, 1984.CrossRefGoogle Scholar
  4. 4.
    L. Friedman, W.L. Bloss, and G. Cooperman, “Enhanced Optical Nonlinearities of Superlattices within the Kronig-Penney Model Incorporating Inherent Bulk Nonlinearities,” J. of Superlattices and Microstructures, to appear.Google Scholar
  5. 5.
    E. Merzbacher, Quantum Mechanics, Second Edition, John Wiley and Sons (1970), p. 100.Google Scholar

Copyright information

© Kluwer Academic Publishers 1985

Authors and Affiliations

  • Gene Cooperman
    • 1
  • Lionel Friedman
    • 1
  • Walter Bloss
    • 1
  1. 1.GTE Laboratories, Inc.WalthamUSA

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