摘要
一维无限深方势阱阱壁的受力计算是量子力学教科书中经常遇见的一个习题,最近其在量子非平衡过程的研究中也吸引了不少研究兴趣.本文提出了一个力算符的定义,利用它可以非常方便地重新得到之前的结果.当阱壁随时间移动时,该算符的正确性也得到了数值验证.这个方法的优点在于避免先引入有限深方势阱计算平均力后再取阱深为无限大的极限过程.计算表明,在量子情形下引入含时正则变换再定义力算符的方法既不正确也无必要.
Calculation of the mean force applied on the wall of one-dimensional infinite square-well potential is an exercise that is frequently met in quantum mechanics textbooks. Recently, it also attracts interesting in the study of quantum nonequilibrium processes. In this paper, a force operator is proposed and is utilized to re-obtain previous result. Its correctness is as well proved in the case of one wall moving at constant velocity. The advantage of the operator is that a process of taking limit does not need, where one has to calculate the mean force for a finite square-well potential first and to take the potential-depth be infinite later. The computations show that, in quantum regime using a time-dependent canonical transformation to define a force operator is neither correct nor essential.
作者
柳飞
赵路
胡磊
LIU Fei;ZHAO Lu;HU Lei(School of Physical Sciences and Nulear Physics, Beihang University, Beijing 100191, China;Laboratory of Fluid Mechanics, School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China)
出处
《大学物理》
2019年第1期1-4,19,共5页
College Physics
基金
北京航空航天大学研究生教育与发展研究专项基金
国家自然科学基金(11174025
11575016
11204154
11574016)
中国科学院创新团队(2060299)资助
关键词
一维无限深方势阱
力算符
相干
one-dimensional infinite square-well potential
force operator
coherent effect
