Abstract: The formalisms of the three representations in quantum mechanics are introduced. They are

Schrdinger representation，Heisenburg representation and interaction representation. The mistakes in some text

books and their reasons are pointed out. A correct expression between the time evolution operators in the

Schrdinger and interaction representations is given. The expression in some text books is wrong because the initial

time is set as zero. The time-dependent perturbation formula is derived.

Key words: Schrdinger representation, Heisenburg representation, interaction representation, perturbation series formula