学术
摘 要:
当薛定谔方程中出现高次非谐振子势,电偶极矩势,分子晶体势,极化等效势等高次正幂与逆幂势函数以及它们的叠加时,薛定谔方程的求解变得非常复杂,采用奇点邻域附近的级数解法与求解渐近解相结合,在多种相互作用幂函数紧密耦合的条件下,得到势函数为V（r）=a1r^6＋a2r^2＋a3r^-4＋a4r^-6的径向薛定谔方程的一系列定态波函数解析解以及能级结构.[著者文摘]
文章出处:
《物理学报》-2007年56卷9期 -5060-5065页
栏目信息:
分 类 号:
The analytic solution of the radial Schrdinger equation for the superposed potential of high-order power and inverse-power potential functions
Hu Xian-Quan, Xu Jie ,Ma Yong ,Yin Lin （ College of Physics and Information Technology, Chongqing Normal University, Chongqing 400047, China）
Abstract:
When the Schrdinger equation involves high-order power and inverse power potential functions or the superposed potential function of high-order anharmonic oscillatory potentials, introduced by the presence of electric dipole moment potential, molecular crystal potential, or the polarized equivalent potential, the solution of the Schrdinger equation becomes very complicated. In this paper, with the help of a combination of series solutions and asymptotic solutions utilized near the singular points, a series analytic solution of the wave functions of stationary state for radial Schrdinger equation with potential function V（r） =a1r^6＋a2r^2＋a3r^-4 ＋a4r^-6 and the corresponding energy level structure are obtained under the tightly-coupled condition of the interacting power potential functions. Meanwhile, the paper gives a proper discussion and some important conclusions are drawn.[著者文摘]
Key words:
solution method using series, power potential function, radial wave function, asymptotic solution
基金资助:
国家自然科学基金（批准号：10147207）,重庆市科委自然科学基金（批准号：2005BB8267）和重庆市教委基础理论研究基金（批准号：KJ060813）资助的课题.
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