一种简捷求解定态薛定谔方程的方法:科尔-霍普夫变换法  

A concise method to solve Schrdinger equation with given potential: method of Cole-Hopf transformation

作　　者：佘守宪[1] 唐莹[1] 

机构地区：[1]北京交通大学物理系,北京100044

出　　处：《大学物理》2004年第12期3-11,共9页College Physics

摘　　要：介绍一种求解各个能级及定态波函数的简捷方法,即借助于科尔-霍普夫(Cole-Hopf)变换法,将给定势函数的定态薛定谔方程变换成黎卡提(Riccati)方程,以求出各个能级及定态波函数.并以谐振子、球谐振子、氢原子、P schl-Teller势、Morse势、Hulth啨n势、双原子分子的三参量势函数、同调谐振子为实例,给出求解方法及结果.By method of Cole-Hopf transformation, Schrdinger equation with given potential is transformed to Riccati equation, and exact energy levels and corresponding wave functions can be obtained in an easy and efficient way. Principle of the method and illustrative examples (harmonic oscillator, spherical harmonic oscillator, Hydrogen atom, Pschl-Teller potential, Morse potential, Hulthén potential, three-parameter potential for diatomic molecules and isotonic harmonic oscillator) are presented.

关 键 词：薛定谔方程 本征值方程 黎卡提方程 科尔-霍普夫变换 能级 定态波函数 

分 类 号：O413.1[理学—理论物理]