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

Gene Cooperman, Lionel Friedman and Walter Bloss
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Gene Cooperman: GTE Laboratories, Inc.
Lionel Friedman: GTE Laboratories, Inc.
Walter Bloss: GTE Laboratories, Inc.

Chapter 19 in Applications of Computer Algebra, 1985, pp 407-414 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-1-4684-6888-5_19

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