基于一维谐振子问题严格解的不确定性关系再讨论  

On Further Studies of Uncertainty Based on the Exact Solution of One-Dimensional Harmonic Oscillator

作　　者：刘家福[1] 张昌芳[1] 曹则贤[2] 

机构地区：[1]装甲兵工程学院基础部,北京100072 [2]中国科学院物理研究所,北京100190

出　　处：《西南师范大学学报（自然科学版）》2014年第7期210-213,共4页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：首先给出了一维谐振子位置和动量算符的不确定度以及它们之间的不确定性关系,发现位置和动量算符的不确定度都随体系能量的增加而增加,这表明关于不确定性关系的两点流行表述,即"某一个量的不确定度变小则另一个量的不确定度必然变大"以及"某一个量的不确定度趋于零时则另一个量的不确定度必然变成无穷大",都是错误的讹传.接着分析了这些讹传发生的起源.此外,还讨论了体系处于所考虑之算符的某个特征状态下因而此力学量的不确定度恒为零的特殊情形,进一步说明不确定性关系不具有原理性的意义.The position and momentum uncertainties for the one-dimensional harmonic oscillator problem have been calculated,both of which have been found to become larger on higher energy levels.It indicates that the two popular statements about the uncertainty relation,i.e,＂the uncertainty of one operator decreases,that of the other must simultaneously increase＂and＂when the uncertainty of one operator becomes vanishing,that of the other must approach infinity＂,are simply misconceptions.The origin of such wrong misconceptions has been analyzed,and,further more,the case has also been discussed that the system is in one of the eigenstates of an operator concerned,thus the uncertainty of this operator is always zero,which thus denies the uncertainty relation given by Heisenberg or Robertson,which again confirms the fact that the uncertainty relation does not cherish any principal meanings.

关 键 词：不确定性关系 不确定度 一维谐振子 严格解 本征态 

分 类 号：G642.0[文化科学—高等教育学]