无穷深势阱中相对论粒子的矩阵元及其经典近似  

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

作　　者：梁麦林[1] 张福林[1] 袁兵[1] 

机构地区：[1]天津大学理学院物理系,天津300072

出　　处：《物理学报》2007年第7期3683-3687,共5页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:20376054)资助的课题.~~

摘　　要：对于无穷深势阱中自旋为0(满足Klein-Gordon方程)和自旋为1/2(满足Dirac方程)的相对论粒子,分别计算了坐标、动量以及速度算符的矩阵元.在大量子数极限下,这些矩阵元给出相应的经典物理量(这里是狭义相对论中的有关量),并且满足正确的经典关系.从而表明,Heisenberg对应原理对这样的相对论体系也适用.For relativistic particles with spin-0 （satisfying the Klein-Gordon equation） and spin-l/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.

关 键 词：无穷深势阱 KLEIN-GORDON方程 DIRAC方程 Heisenberg对应原理 

分 类 号：O413.1[理学—理论物理]