量子隧穿效应及其在波包隧穿中的数值计算

Quantum Tunneling Effect and Numerical Calculation in Wave Packet Tunneling

文章利用量子力学隧穿中的基本原理,通过对简单势进行推广,利用传递矩阵的方法求解一般势垒下粒子的透射率.计算模拟了给定波包穿过任意势能函数下的波函数空间部分与动量分布随时间演化的关系,可以求解一般势函数下的粒子隧穿情况.通过所设计的程序发现并验证了粒子的共振隧穿效应,观测到透射率的震荡现象,对于分析实际量子隧穿过程提供了模拟算法.

This paper uses the basic principles of quantum mechanics tunneling,generalizes simple poten⁃tials,and uses the transfer matrix method to calculate the transmittance of particles under general barriers.At the same time,we calculated and simulated the relationship between the wave function of the specified wave packet passing through an arbitrary potential energy function and the evolution of momentum distribution over time,which can be used to solve the particle tunneling under the general potential function.Through the de⁃signed program,the resonant tunneling effect of particles is discovered and verified,and the oscillation phe⁃nomenon of transmittance is observed,which provides a simulation algorithm for analyzing the actual quantum tunneling process.