<論文>単一禁制帯を与えるポテンシャルの検討

概要

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Potentials with a single forbidden band have been shown to satisfy a nonlinear differential equation. The equation is satisfied by elliptic functions of order 2 with a double pole in a period parallelogram with a suitably adjusted multipilcative constant. We show that the functions cannot be odd functions and that if they are even, then their pole's location is restricted to the origin or a half period point in the fundamental period parallelogram. A primary condition for such functions to be a potential with a single forbidden band is that they are real and periodic on the real axis. From this condition, it has been found that, if one of the period of these elliptic functions is a real and another one is a pure imaginary, then their zeros must be on lattice by periods and half periods. Based on these results, we derive a class of functions with a single forbidden band.
北海道東海大学の論文
1990-03-20