一维无限深梯形势阱中微观粒子波函数和能级的数值解和变分解  

Numerical and variational solution of wave functions and energy levels of the micro-particle in the one-dimensional infinite trapezoid potential well

作　　者：罗强[1] 姜玉梅[1] 苏垣昌[1] 韩玖荣[1] 

机构地区：[1]扬州大学物理科学与技术学院,江苏扬州225002

出　　处：《大学物理》2014年第11期54-58,共5页College Physics

摘　　要：介绍了一种用来求解二阶常微分方程边值问题的算法,即著名的Numerov算法,并通过这种算法和打靶法得到了一维无限深梯形势阱中粒子波函数和能级的数值解.此外构造了幂函数和三种统计分布乘积形式的试探波函数,通过变分法得到了一维无限深梯形势阱的基态能.We introduce an algorithm, namely the celebrated Numerov algorithm, which is used to solve boundary value problem of two-order ordinary differential equation, and we obtain the numerical solution of the wave functions and energy levels of the particle confined into the one dimensional infinitely trapezoid potential well along with the shooting method. Besides, we get the ground state energy of the model through variational method.

关 键 词：薛定谔方程 梯形势阱 Numerov算法 变分法 

分 类 号：O413.1[理学—理论物理]