摘要
讨论了一维对称简谐势的薛定鄂方程的通解,通解可用抛物线柱函数Dα(t)来表示,且可由Kummer函数表达,Hermite多项式表示的一维简谐势的解仅是该通解的一特殊形式。此通解用于一维对称双势阱模型的讨论,此模型由两相同的简谐势连接而成,得出了此模型的精确解。作为一例,本文给出了一具体模型的精确数值结果。
The general solution of the Schroedinger equation for the harmonic potential in onedimension is studied, which can be expressed by the parabolic cylinder function Dα(t) and also by the Kummer's function, rather than by the Hermite function. It is pointed out that the Hermite function is only a special form of the general solution for the potential. A doublewell potential is exactly solved by this way, which involves two symmetrically identical harmonic potentials. A precise numerical solution is given as an example for a typical doublewell potential.
出处
《贵州工业大学学报(自然科学版)》
CAS
2003年第2期1-4,共4页
Journal of Guizhou University of Technology(Natural Science Edition)
基金
贵州省科技基金[黔基计字(2002)3024]