量子力学表示理论的一种实现  

A realization of representation theory

作　　者：汪克林[1] 曹则贤[2] WANG Ke-Lin;CAO Ze-Xian(Department of Modern Physics,University of Science and Technology of China,Hefei 230026,China;Institute of Physics,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]中国科学技术大学近代物理系,合肥230026 [2]中国科学院物理研究所,北京100190

出　　处：《物理》2024年第3期168-173,共6页Physics

摘　　要：量子力学创立伊始,狄拉克就关注到了一般表示的问题,其后量子力学的发展又引入了福克态、相干态等表示。好的表示应能提供正交归一的完备基,同时又能给出问题的严格解析解或者允许方便地得到近似解,但这常常是做不到的。我们意识到此前得到的相干态正交化方法恰恰满足表示理论的一般性要求,且因为包含自由参数为构造归一化的完备正交基实际上提供了无限的选择,这样甚至在解决问题的过程中都可以灵活地选择不同的表示,从而带来计算量的大幅减小。通过对不同耦合强度下的近共振态Rabi模型最初10个能级的计算,并同关联的JC模型的结果相比较,验证了相干态正交化方法的有效性。Just when quantum mechanics was created,Dirac discussed the representation theory for it,and later it evidenced the introduction of representations based on Fock states,coherent states,etc.A good representation should provide a complete set of orthonormal basis functions,which allows for an analytical solution of the problem,or the easy attainment of numerical approximation,but it is,however,usually unrealizable.The normalized coherent states we achieved before meet the requirements upon a good representation,in fact,they even provide infinite possibilities for setting up a complete set of orthonormal basis functions since it contains free parameters,thus allowing for choosing alternative representations in due course of attacking a problem,which in turn significantly reduces the computational demands.The first ten energy levels for the Rabi model in the near resonance configuration,with different coupling strengths,were calculated and brought into comparison with that for JC model,the results,as anticipated,confirmed the effectiveness of our method.

关 键 词：表示理论 归一化完备正交基 相干态 相干态正交化 Rabi模型 

分 类 号：O413.1[理学—理论物理]