Matrix elements and classical limit of relativistic particles in infinitely deep potential well

Abstract

For relativistic particles with spin-0 (satisfying the Klein-Gordon equation) and spin-1/2 (satisfying the Dirac equation) in infinitely deep potential well, matrix elements for the coordinate, momentum and the velocity operators are calculated. In the limit of large quantum numbers, these matrix elements give the corresponding classical quantities (nowbeing related quantities in special relativity) and satisfy exact classical relations. These results show that the Heisenberg correspondence principle is applicable to such relativistic systems.