超對稱能勢在超晶格上的應用及庫倫勢雜質在有現量子線上的效應

Abstract

超對稱在物理學上是一種很優美的方法，它描述一對超對稱能勢具有幾近 乎全同本徵值及它們的本徵函數之間的關係，利用此種近乎全同本徵值的 特性，可讓我們逐步建構一種屬於高能階的膺勢，在利用此種超對稱關係 於固態物理學上，我們可以建構出屬於高能帶的膺勢去處理我們較感興趣 的問題。我們將使用李榮章先生所提的方法於一種位阱超晶格去討論研究 該方法的可行性。庫倫勢雜質在量子線上有著和二､三維空間非常迥異的 特性，我們將先對前人所做過的研究做回顧，同時，因庫倫勢之奇異性所 引起的一些效應將見於本篇論文之中。 Supersymmetric quantum mechanics (SUSY QM) is an elegant methodology in physics. It describes the isospectrum of a pair partner potential and the relationship between theireigenfunctions. With this characteristic isospectrum one can construct a pseudopotential of a given potential step-by- step to remove its lower energy levels into higher stairs. Applying this method to solid state physics, one can also drop those lower bands to exercise our work on our interested problems. We will follow the supersymmetric pseudopotential, which suggested by Y.C.Lee et al. and use a square well superlattice to check whether if such a method has its validity in application to solid state physics. And another independent topic puts inthis thesis. We consider the problem of a Coulomb potential type impurity in a finite quantum line. For an one- dimensional Coulombpotential has a singularity, playing very much different withthat of two or three dimensional ones, has been shown in ourntent. That reflects an unusual interesting phenomenon foundis theis.