绍兴文理学院学报
紹興文理學院學報
소흥문이학원학보
Journal of Shaoxing University
2009年
8期
23-26
,共4页
Kratzer势%Schr(o)dinger方程%Laplace变换%递推关系
Kratzer勢%Schr(o)dinger方程%Laplace變換%遞推關繫
Kratzer세%Schr(o)dinger방정%Laplace변환%체추관계
Kratzer potential%Schr(o)dinger equation%Laplace transformation%recursive relation
求解了Kratzer势的Schr(o)dinger方程,得到了归一化的波函数和能量方程.用Laplace变换使径向的二阶微分方程退化为一阶微分方程,直接积分后用级数展开,应用Laplace逆变换得出本征函数.另外,用Laplace变换方法给出了径向波函数关于量子数N和角量子数L的二类递推关系.
求解瞭Kratzer勢的Schr(o)dinger方程,得到瞭歸一化的波函數和能量方程.用Laplace變換使徑嚮的二階微分方程退化為一階微分方程,直接積分後用級數展開,應用Laplace逆變換得齣本徵函數.另外,用Laplace變換方法給齣瞭徑嚮波函數關于量子數N和角量子數L的二類遞推關繫.
구해료Kratzer세적Schr(o)dinger방정,득도료귀일화적파함수화능량방정.용Laplace변환사경향적이계미분방정퇴화위일계미분방정,직접적분후용급수전개,응용Laplace역변환득출본정함수.령외,용Laplace변환방법급출료경향파함수관우양자수N화각양자수L적이류체추관계.
In this paper the exact bound state solutions including the energy equation and normalized wave function of Schrdinger equation with the Kratzer potential is obtained.By using the Laplace transformation this second-order differential equation can be reduced to the first-order case and then the eigenfunction can be derived from direct integral and a simple series expansion via Laplace inverse transform.In addition,two kinds of recursive relations about the principle and angular quantum numbers N and L for the radial wave function are also given by using the same method.
