Quantum mechanical version of the classical Liouville theorem  

作　　者：谢传梅 范洪义 

机构地区：[1]College of Physics & Material Science,Anhui University [2]Department of Material Science and Engineering,University of Science and Technology of China

出　　处：《Chinese Physics B》2013年第3期201-204,共4页中国物理B（英文版）

基　　金：Project supported by the Doctoral Scientific Research Startup Fund of Anhui University,China (Grant No. 33190059);the National Natural Science Foundation of China (Grant No. 10874174);the Research Fund for the Doctoral Program of Higher Education of China (New Teacher) (Grant No. 20113401120004);the Open Funds from the National Laboratory for Infrared Physics,Chinese Academy of Sciences (Grant No. 201117)

摘　　要：In terms of the coherent state evolution in phase space,we present a quantum mechanical version of the classical Liouville theorem.The evolution of the coherent state from ｜z〉to｜sz-rz＊〉 corresponds to the motion from a point z（q,p） to another point sz-rz＊ with ｜s｜2-｜r｜2=1.The evolution is governed by the so-called Fresnel operator U（s,r） that was recently proposed in quantum optics theory,which classically corresponds to the matrix optics law and the optical Fresnel transformation,and obeys group product rules.In other words,we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space,which seems to be a combination of quantum statistics and quantum optics.In terms of the coherent state evolution in phase space,we present a quantum mechanical version of the classical Liouville theorem.The evolution of the coherent state from ｜z〉to｜sz-rz＊〉 corresponds to the motion from a point z（q,p） to another point sz-rz＊ with ｜s｜2-｜r｜2=1.The evolution is governed by the so-called Fresnel operator U（s,r） that was recently proposed in quantum optics theory,which classically corresponds to the matrix optics law and the optical Fresnel transformation,and obeys group product rules.In other words,we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space,which seems to be a combination of quantum statistics and quantum optics.

关 键 词：Fresnel operator Liouville theorem quantum mechanical version 

分 类 号：O413.1[理学—理论物理] O175.25[理学—物理]