量子与经典对应:Dirac方程中的速度算符  

Quantum and classical correspondence for velocity operator in Dirac equation

作　　者：张治国[1] 封文江[1] 郑伟[1] 陈皓[1] 崔崧[1] 

机构地区：[1]沈阳师范大学物理科学与技术学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2016年第4期441-444,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省教育厅科学研究一般项目(L2014442)

摘　　要：由量子力学中的Bohr对应原理可知,在大量子数情形下,量子力学应过渡到经典力学。在经典极限下,由Heisenberg对应原理可知,厄密算符的量子矩阵元对应经典物理量的Fourier展开系数。利用Heisenberg对应原理研究相对论效应的自由粒子和在匀磁场中的带电粒子的量子经典对应问题。将Heisenberg对应原理应用到相对论领域的Dirac方程,计算出自由粒子的Dirac方程中的α算符及其经典近似,并且研究自旋1/2的带电粒子在匀磁场中的Dirac方程情形。对于相对论效应的自由粒子和在匀磁场中的带电粒子,Dirac理论中的α算符将对应经典的速度。Due to Bohr correspondence principle in the quantum mechanics,quantum mechanics go to classical mechanics in the case of large quantum number. Based upon Heisenberg correspondence principle,quantum matrix element of a Hermitian operator reduces to the coefficient of Fourier expansion of the corresponding classical quantity in the classical limit.Using Heisenberg correspondence principle,quantum-classical correspondence of the relativistic free particle and the 1/2spin charged particles in a constant magnetic field are studied.Applying Heisenberg correspondence principle to Dirac equation in relativistic realm,the operator of free particle in the Dirac theory and quantum-classical correspondence are obtained,and 1/2spin charged particle in a constant magnetic field in Dirac equation is also studied.For the relativistic free particle or the charged particle in a constant magnetic field,the velocity operator in the Dirac theory will reduce to the classical velocity.

关 键 词：Heisenberg对应原理 DIRAC方程 速度算符 

分 类 号：O413.1[理学—理论物理]