物理与工程2025，Vol.35Issue(1)：52-57,6.
提升量子力学中表象变换的理解
IMPROVE PERCEPTION TOWARD REPRESENTATION TRANSFORMATION IN QUANTUM MECHANICS
摘要
Abstract
In this paper,the method how to further study the representational and the repre-sentational transformation is introduced by geometry coordinates,linear algebra and physical concept.According to this representational theory which can be simply compared with coordi-nate theory in geometry,two simple memory methods have been provided.Firstly,the trans-formation formula can be written as b=S+a from representation A to representation B,in which the matrix element of the transformation matrix is<ψ|φ>,which can be regarded as the inner product between the basis vector of representation A and representation B.At the same time,this formula can be thought of as the expression of the representation B of the state vec-tor equals the transformation matrix acting on the expression of the representation A.Second-ly,the transformation formula can be written as F'=S+FS for the mechanical operator from representation A to representation B,in which the operator F and operator F'are the expres-sion of representations A and representations B,respectively,which this formula can be thought of as the expression of the representation B of the mechanical operator equals the con-jugate matrix of transformation matrix and the expression of the representation A of the me-chanical operator acting on transformation matrix.Finally,an example is given to prove the superiority of representation transformation.Meanwhile,the intrinsic function under two rep-resentations is deduced and the transformation between them is realized by the Fourier trans-form,thus deepening the understanding of representation transformation.关键词
表象变换/希尔伯特空间/表象定义/幺正变换Key words
representation transformation/Hilbert space/definition of representation/unita-ry transformation引用本文复制引用
周琪琪,郭立帅..提升量子力学中表象变换的理解[J].物理与工程,2025,35(1):52-57,6.基金项目
甘肃省高等学校创新基金项目(2022A-128) （2022A-128）
庆阳市科技计划项目(QY-STK-2022A-024). （QY-STK-2022A-024）
