Exact Solutions for Superlattices and How to Recognize them with Computer Algebra
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.
KeywordsHigh Order Term Computer Algebra Schrodinger Equation Apply Physic Letter Important Special Case
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