IMPROVE PERCEPTION TOWARD REPRESENTATION TRANSFORMATION IN QUANTUM MECHANICS

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.