Authors: shuang-ren Zhao
Quantum mechanics offers us the quantization. The quantization offer us a method from the mechanic equation to build the quantum wave equation. For example the Canonical quantization offers a method to build the Schrödinger equation from Hamilton in classical mechanics this is also referred as first quantization. In general Maxwell equation itself is wave equation, hence it doesn't need the first quantization. There is second quantization for electromagnetic field. The second quantization discuss how many photons can be created when the energy of electromagnetic field is known. This is not interesting to this author. This author is interested how we can build the particle from the wave equations (Maxwell equations or Schrödinger equation). Here the particle should confined in space locally. It should has the properties of wave. Our traditional quantization is to find the wave equation. This author try to build a particle from this wave equation, this process can be called as particleization. Abstract This author has introduced the mutual energy principle, the mutual energy principle successfully solved the problem of conflict between the Maxwell equations and the law of the energy conservation. The mutual energy flow theorem is derived from the mutual energy principle. The mutual energy flow is consist of the retarded wave and the advanced wave. The mutual energy flow theorem tell us the total energy of the energy flow goes through any surfaces between the emitter to the absorber are all same. This property is required by the photon and any quantum. Hence, this author has linked the mutual energy principle to the photon. The mutual energy flow has the property of wave and also confined in space locally. However there is still a problem, the field of an emitter or the field of an absorber decreases according to the distance. If the current of a source or sink for a photon is constant. The energy of the photon which equals the inner product of the current and the field will depended on the distance between the the source and the sink of the photon. If the distance increases, the amount of photon energy will decrease to infinite small. This is not correct. The energy of a photon should be a constant E=hv. The energy of the photon cannot decrease with the distance between the emitter and the absorber. In order overcome this difficulty, this author make a normalization for the mutual energy principle. It is assume that the retarded wave sent from the emitter has collapse back in all direction. But the mutual energy flow build a channel between the source and sink. Since the energy can only go through this channel, the total energy of a photon must go through this channel. Hence, the total energy of the mutual energy flow has to be normalized to the energy of one photon. The wave energy will increased in the direction of the channel. The amplitude of the wave does not decrease on the direction along the channel. The advanced wave also does not decrease on the direction of the channel. The electromagnetic wave in the space between an emitter (source) and an absorber (sink) look like a wave inside a wave guide. The wave in a wave guide, the amplitude does not decrease alone the wave guide if the loss of energy can be omitted. This wave guide can be called the nature wave guide. In the wave guide the advanced wave leads the the retarded wave, hence, the retarded wave can only goes at the direction where has strong advanced wave. This normalization process successfully particularized the the mutual energy flow.
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