Abstract: In quantum mechanics, Schrödinger equation is used to describe how the motion of microscopic particles changes with time, and its significance is self-evident. In traditional teaching, Schrödinger equation is usually introduced directly as a definition, or gradually guided and established by the wave-particle duality of experimental facts. However, the traditional guidance and construction methods have certain leaps, their logic is not rigorous, and they lack deep-seated principle support, which is not conducive to the in-depth understanding of some students. The purpose of this paper is to start from the deep-seated theoretical framework of symmetry and one-to-one correspondence of conservation quantities, carries out mathematical derivation on the basis of Taylor^,s expansion, and gradually introduces Schrödinger equation on the basis of students^, quantum mechanics and mathematical knowledge. Firstly, we introduce the traditional introduction methods. Secondly, on the basis of reviewing Taylor^,s expansion, we introduce Taylor^,s translation concept, which forms an organic combination of old and new knowledge and further stimulates students^, creative thinking. Finally, the Schrödinger equation is naturally derived by using the concept of Taylor^,s translation and Noether^,s theorem.

Key words: Noether^,s theorem, Taylor^,s expansion, Schr?dinger equation, Taylor^,s translation, creative thinking