Abstract: The solution of time dependent Schrödinger equation in a one-dimensional homogeneous field is carried out in detail. The idea is, based on the classical trajectory of a classical particle in the homogenous filed, the time dependent wave function can be constructed from this trajectory with a phase factor function which is determined by solving the Schrödinger equation. Guided by this idea,  the propagator function of homogeneous field is obtained for both position representation and momentum representation. Meanwhile, Dirac notation for state vectors is employed to obtain the above results for comparison.

Key words: Schr?dinger equation, position representation, momentum representation, Dirac notation for state vectors, propagator function