In this work a new representation of quantum mechanics, that is, the electromagnetic field representation, is proposed, which is different from the Schr dinger`s equation and Heisenberg`s Matrix. It is pointed out that even though the results from Schr dinger`s equation, Heisenberg`s Matrix and electromagnetic field representation in describing the quantum system are the same, the principles and procedures in describing the quantum system are totally different. The further result regarding the application of the electromagnetic field representation of quantum mechanics to different atomic and molecular systems will be presented later.