演示环境（数据为演示用途，非真实数据）

本文主要介绍了如何从几何坐标、线性代数和物理学角度出发去加深对表象及表象变换的理解，并将表象变换理论与几何中的坐标理论进行类比，给出了两种表象变换公式的记忆方法，一个是态矢量从A表象到B表象的变换公式b=S~+a,变换矩阵的矩阵元为〈ψ|φ〉,可将其看成A表象的基矢与B表象的基矢构成的内积，此时公式理解为态矢量在B表象中的表示等于将变换矩阵的共轭矩阵作用在态矢量在A表象中的表示上；另一个是力学量算符从A表象到B表象的变换公式F′=S~+FS,其中F、F′分别为算符在A、B表象中的表示，则可将公式理解为算符在B表象中的表示等于变换矩阵的共轭矩阵和算符在A表象中的表示作用在变换矩阵上。最后本文通过例题证明了表象变换的优越性，同时推导了两种表象下的本征函数，并用傅里叶变换实现了它们之间的转换，从而加深了对表象变换的理解。

In this paper, the method how to further study the representational and the representational transformation is introduced by geometry coordinates, linear algebra and physical concept. According to this representational theory which can be simply compared with coordinate theory in geometry, two simple memory methods have been provided. Firstly, the transformation 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 vector equals the transformation matrix acting on the expression of the representation A. Secondly, 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 expression 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 conjugate matrix of transformation matrix and the expression of the representation A of the mechanical operator acting on transformation matrix. Finally, an example is given to prove the superiority of representation transformation. Meanwhile, the intrinsic function under two representations is deduced and the transformation between them is realized by the Fourier transform, thus deepening the understanding of representation transformation.