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.
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References
Dohler, Gottfried, “Solid-State Superlattices,” Scientific American, 249(5), pp. 144–151, Nov., 1983.
W.L. Bloss and L. Friedman, Applied Physics Letters, Vol. 41(11), p. 1023, 1982.
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.
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.
E. Merzbacher, Quantum Mechanics, Second Edition, John Wiley and Sons (1970), p. 100.
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© 1985 Kluwer Academic Publishers
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Cooperman, G., Friedman, L., Bloss, W. (1985). Exact Solutions for Superlattices and How to Recognize them with Computer Algebra. In: Pavelle, R. (eds) Applications of Computer Algebra. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-6888-5_19
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DOI: https://doi.org/10.1007/978-1-4684-6888-5_19
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-6890-8
Online ISBN: 978-1-4684-6888-5
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