一种光滑连续双势阱模型的精确求解  

Exact Solution for a Kind of Smoothly Joined Double-Well Potential

作　　者：朱涛[1] 刘克家[1] 王金凤[1] 

机构地区：[1]贵州工业大学冶金系,贵州贵阳550003

出　　处：《贵州工业大学学报（自然科学版）》2003年第6期14-17,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20023024);贵州省教育厅基金(20022307)

摘　　要：构造并精确求解了一种新的双势阱模型,它由三段曲线势函数光滑连接而成。此三段势能均具有一维势能1/2KX2的形式,讨论了K∈R情况下势能1/2KX2的通解,通解为实函数,且可用Kummer函数来表示。给出了一个具体双势阱模型精确解,即获得了模型的能量本征值,及对应的波函数。A new kind of double-well potential is studied, which is smoothly joined by three piecewise potentials with the form 1/2kx2 (k∈R) in one-dimension. We solved and discussed in detail the Schroedinger equation for the potential 1/2kx2(for k∈R). The general solution for the equation is a real function and can be expressed by Kummer's function. The exact solution for a typical double-well potential,i. e. ,a precise numerical solution for the eigen-value,as well as the eigen-function, is given.

关 键 词：光滑连续双势阱模型 势能 Kummer函数 波函数 量子力学 薛定鄂方程 

分 类 号：O413.1[理学—理论物理]