大学物理 ›› 2014, Vol. 33 ›› Issue (11): 54-54.
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罗强 姜玉梅 苏垣昌 韩玖荣
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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.
关键词: 薛定谔方程, 梯形势阱, Numerov算法, 变分法
Abstract: 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.
Key words: Schrodinger＇ s equation, trapezoid potential well, Numerov algorithm, variational method
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罗强 姜玉梅 苏垣昌 韩玖荣. 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[J]. 大学物理, 2014, 33(11): 54-54.
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https://dxwl.bnu.edu.cn/CN/Y2014/V33/I11/54
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