回路积分形式的量子力学表象及其应用  

Quantum Mechanical Representation of Loop Integral Form and Its Application

作　　者：陈锋[1] CHEN Feng(Institute of Advanced Manufacturing Engineering,Hefei University,230022,Hefei,Anhui,China)

机构地区：[1]合肥学院先进制造工程学院,安徽合肥230022

出　　处：《淮北师范大学学报（自然科学版）》2023年第3期36-40,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省高校协同创新项目(GXXT-2022-050)。

摘　　要：在量子力学中关于逆算符的本征态求解问题是教学难点之一。为解决这一难题,文章在分析量子力学表象完备性的回路积分形式后,证明量子态本征矢是相干态和产生算符本征态构成。进一步推导,首次得到产生算符逆算符在福克空间的具体形式。另外,基于有序算符内的积分技术和回路积分形式,给出了压缩变换下产生算符的逆算符及对应的压缩粒子数态的显式。通过回路积分形式的量子力学表象分析,可以丰富和扩展关于量子力学基本概念的教学内容。Solving the eigenstates of inverse operators is one of the difficult teaching problems in quantum mechanics.To solve this problem,the eigenvector of quantum states is proved to be composed of coherent states and eigenstates of production operators after analyzing the loop integral form of representation com⁃pleteness in quantum mechanics.Furthermore,the concrete form of the generating operator and the inverse operator in Fock space are obtained for the first time.In addition,the inverse operator of the generated opera⁃tor under the compression transformation and the corresponding number state of the compressed particle are given based on the integration technique in the ordered operator and the loop integration form.The teaching content of the basic concepts of quantum mechanics can be enriched and expanded via the representation analysis of quantum mechanics in the form of loop integration.

关 键 词：回路积分 逆算符 本征态 

分 类 号：G64[文化科学—高等教育学]