刚性对称陀螺分子Stark效应的精确解  

Exact solutions to Stark effect of rigid symmetric-top molecules

作　　者：陈昌远[1] 孙国华 王晓华[1] 孙东升[1] 尤源[1] 陆法林 董世海 Chen Chang-Yuan;Sun Guo-Hua;Wang Xiao-Hua;Sun Dong-Sheng;You Yuan;Lu Fa-Lin;Dong Shi-Hai(School of Physics and Electronic Engineering,Yancheng Teachers University,Yancheng 224007,China;Catedrática CONACYT,CIC,Instituto Politécnico Nacional,CDMX 07700,Mexico;Research Center for Quantum Physics,Huzhou University,Huzhou 313000,China;Laboratorio de Información Cuántica,CIDETEC,Instituto Politécnico Nacional,UPALM,CDMX 07700,Mexico)

机构地区：[1]盐城师范学院物理与电子工程学院,盐城224007 [2]Catedrática CONACYT,CIC,Instituto Politécnico Nacional,CDMX 07700,Mexico [3]湖州师范学院量子物理研究中心,湖州313000 [4]Laboratorio de Información Cuántica,CIDETEC,Instituto Politécnico Nacional,UPALM,CDMX 07700,Mexico

出　　处：《物理学报》2021年第18期1-9,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11975196);墨西哥国立理工大学基金(批准号:20210414)资助的课题.

摘　　要：提出了一种精确求解位于外电场中刚性对称陀螺分子转动能级和相应解析波函数的新方法.首先利用不同形式的函数变换和变量代换将位于外电场中对称陀螺分子的极角θ方向的方程转化为合流Heun微分方程,然后根据合流Heun微分方程和合流Heun函数具有的特点,找到描述同一本征态的线性相关的两个解,构造Wronskian (朗斯基)行列式,得到精确的能谱方程.最后利用Maple软件计算出不同量子态的本征值,再将得到的本征值代入本征函数进行归一化运算最终得到用合流Heun函数表示的解析的归一化本征函数.这些结果可为深入研究对称陀螺分子的Stark效应提供有益的帮助.In this work a new scheme is proposed to accurately calculate the rotational energy level of the rigid symmetric-top molecule subjected to the external electric field, and also to obtain the corresponding analytical wave functions. For this purpose, first we use the different forms of function transformation and variable substitution to transform the differential equation of the polar angle θ into a confluent Heun differential equation, and then we use the characteristics of the confluent Heun differential equation and the confluent Heun function to find two linearly dependent solutions of the same eigenstates, which are used to construct the Wronskian determinant to obtain the exact energy spectrum equation. Finally, with the aid of the Maple software, we calculate the eigenvalues for different quantum states, and then substitute the obtained eigenvalues into the unnormalized eigenfunction to obtain the analytical normalized eigenfunction expressed by the confluent Heun function. These results are conducive to the in-depth study of the Stark effect of symmetric-top molecules.

关 键 词：精确解析解 STARK 效应 刚性对称陀螺分子 合流 Heun 函数 

分 类 号：O641[理学—物理化学]