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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Kluwer Academic Publishers
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive