基于测不准原理的一维谐振子势中粒子能级及概率的讨论  

Discussion of the Particle Level and Probability in One Dimensional Harmonic Oscillator Potential Based on Uncertainty Principle

作　　者：代君瑶 张澜旭 温莹 张海丰[1] DAI Junyao;ZHANG Lanxu;WEN Ying;ZHANG Haifeng(College of Natural Science,Jiamusi University,Jiamusi Heilongjiang 154007,China;College of Mechanical Engineering,Jiamusi University,Jiamusi Heilongjiang 154007,China)

机构地区：[1]佳木斯大学理学院,黑龙江佳木斯154007 [2]佳木斯大学机械工程学院,黑龙江佳木斯154007

出　　处：《佳木斯大学学报（自然科学版）》2021年第5期168-170,共3页Journal of Jiamusi University：Natural Science Edition

基　　金：黑龙江省省属本科高校基本科研业务费科研项目资助(2019-KYYWF-1363);佳木斯大学大学生创新创业训练计划项目(S202110222127)。

摘　　要：通过代数解法求解了一维线性谐振子的定态薛定谔方程,给出了粒子在不同能级下出现的概率,进而利用测不准原理分析了一维线性谐振子基态能级。研究结果表明:能级越高粒子出现的概率越小,粒子越趋于经典物理行为;测不准关系对于估算基态能级和精确求解一致。The fixed state Schrodinger equation of a one-dimensional linear harmonic oscillator is solved by algebraic method,and the probability of particles appearing at different energy levels is given.And then the ground state energy levels of a one-dimensional linear harmonic oscillator are analyzed by means of uncertainty relation.The results show that the higher the energy level is,the smaller the probability is,and the more the particle tends to the classical physical behavior.And the estimation of the uncertainty relation is consistent with the exact solution for the ground state energy level.

关 键 词：一维线性谐振子 能级 测不准原理 

分 类 号：O431[机械工程—光学工程]