The solution of Schrödinger  equation for free particle and one-dimensional infinite potential well is

the basic content of quantum mechanics. In this paper， Fourier transform is used to solve these two

simple Schrödinger equations. Through the in-depth discussion of the Fourier transform method of partial differential equation and the Fourier transform method of ordinary differential equation which separates from the partial differential equation by separated variable method，the results are consistent with those of relevant textbooks，and the differences and relations between the two methods are discussed.