李重石. 粒子在解析势场中的能级[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 1984, (2).DOI:
粒子在解析势场中的能级
摘要
解析势 V(x)=f(x)
可以展为泰勒级数
如果
f″(a)>0
将其前三项视为0级哈密顿算符 H0
它相当于谐振子势
后面高次项视为微扰 H′处理
则解析势束缚态问题可解
并可逐次提高近似程度。本文用占有数表象讨论
问题更简化
现讨论于后.(一)基本方法设有一解析函数势 V(x)=f(x).在其解析区域内 x=a 点展开
得于是取为0级哈密顿量.若 f″(a)>0
则 H0是谐振子哈密顿量
粒子处于束缚态.其 k=f″(a).
Abstract
It is reported in this paper that analytic potential V(a)may be extended to Taylor's series.The three anterior terms of this series may be regardes as a linear harmanic oecillation while the posterior terms as perturbation.It has been solved by means of using the method of occupied number represeutation. The equation V(x)=-V0 ch-2x/a has been solved in paper.The resent ap- porximates to perfection.It is better than the W.K.B Method
and example two is a close approximation to perfection