College Physics ›› 2019, Vol. 38 ›› Issue (1): 1-.doi: 10.16854 /j.cnki.1000-0712.170621

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Force operator in one-dimentional infinite square-well potential

LIU Fei1,ZHAO Lu1,HU Lei2   

  1. 1. School of Physical Sciences and Nulear Physics,Beihang University,Beijing 100191,China; 2. Laboratory of Fluid Mechanics,School of Aeronautic Science and Engineering,Beihang University,Beijing 100191,China
  • Received:2017-11-15 Revised:2018-06-19 Online:2019-01-20 Published:2019-02-27

Abstract: 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.

Key words: one-dimensional infinite square-well potential, force operator, coherent effect