New quantum mechanical model  

作　　者：吴宁 阮图南 

机构地区：[1]CCAST(World Lab), P.O.Box 8730, Beijing 100080, China [2]Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China

出　　处：《Science China Mathematics》1996年第10期1106-1111,共6页中国科学：数学（英文版）

基　　金：Project supported in part by the Foundation of Ph.D.Directing Program of Chinese University,Prof.T.D.Lee's NNSC Grant;the National Natural Science Foundation of China and grant LWTV/1298 of Chinese Academy of Sciences.

摘　　要：A quantum mechanical model with one bosonic degree of freedom is discussed in detail. Conventionally, when a quantum mechanical model is constructed, one must know the corresponding classical model. And by applying the correspondence between the classical Poisson brackets and the canonical commutator, the canonical quantization condition can be obtained. In the quantum model, study of the corresponding classical model is needed first. In this model, the Lagrangian is an operator gauge invariant. After localization, in order to keep gauge invariance, the operator gauge potential must be introduced. The Eular-Lagrange equation of motion of the dynamical argument gives the usual operator equation of motion. And the operator gauge potential just gjves a constraint. This constraint is just the usual canonical quantization condition.A quantum mechanical model with one bosonic degree of freedom is discussed in detail. Conventionally, when a quantum mechanical model is constructed, one must know the corresponding classical model. And by applying the correspondence between the classical Poisson brackets and the canonical commutator, the canonical quantization condition can be obtained. In the quantum model, study of the corresponding classical model is needed first. In this model, the Lagrangian is an operator gauge invariant. After localization, in order to keep gauge invariance, the operator gauge potential must be introduced. The Eular-Lagrange equation of motion of the dynamical argument gives the usual operator equation of motion. And the operator gauge potential just gjves a constraint. This constraint is just the usual canonical quantization condition.

关 键 词：operator-valued GAUGE transformation CANONICAL QUANTIZATION condition HERMITICITY REQUIREMENT OPERATOR GAUGE potential. 

分 类 号：O413.1[理学—理论物理]