**Authors:** Shuang-ren Zhao

This author has replaced the Maxwell equations with the corresponding mutual energy principle, self-energy principle as the axioms in electromagnetic field theory. The advantage of doing this is that it can overcome the difficulty of the Maxwell equations, which conflicts to the energy conservation law. The same conflict also exists in the Schrödinger equation in the quantum mechanics. This author would like to intruded the mutual energy principle to quantum mechanics, but has met the difficulty that there is no advanced solution for the Schrödinger equation. This difficulty is overcome by introducing a negative radius. After this, all the theory about the mutual energy can be extend from the field satisfying Maxwell equations to the field satisfying Schrödinger equation. The Schrödinger equation can also be derived from the corresponding mutual energy principle. However, this doesn't mean both sides are equivalent. The mutual energy principle cannot derive a single solution of Schrödinger equation. The mutual energy principle can only derive a pair solutions of the Schrödinger equations. One is for retarded waves and another is for advanced waves. The retarded wave and the advanced wave must be synchronized. The solutions of the mutual energy principle is in accordance with the theory of the action-at-a-distance and the absorber theory. A action is done always between two objects, for example a source (emitter) and a sink (absorber). The mutual energy principle tell us that a particle is an action and a reaction between the source and the sink. In other hand the wave satisfying Schrödinger equation only need one source or one sink. From the mutual energy principle, it is easy to derive the mutual energy theorem, the mutual energy flow theorem, corresponding Huygens–Fresnel principle. All these will solve the wave-particle duality paradox.

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[v1] 2019-08-25 11:05:19

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