The theory of representation is an important part of quantum mechanics and is difficult to study.This paper deeply analyzes and discusses the characteristics and laws of representation transformation,detailed describes the inner relationship be-tween the expressions of quantum states and mechanical-quantity operators in two different representations,uncovers the fea-tures of unitary-transformation matrices and puts forward a simple method for firmly memorizing the formulae of unitary trans-formation.These findings would contribute to understanding and memorizing the transforming relationship o...