Other chemical reactions typically involve similar amounts of energy. Radioactive decay gamma rays are considered as part of nuclear physics , rather than high energy physics. The proton has a mass of around 9. Due to these very high energies at the single particle level , particle physics is, in fact, high-energy physics.
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It can be made in an analogous way for the corresponding quantities for the total particle ensemble denoted with the index tot. In the calculations above we found the formula in Eq. Since these equations are similar to results stated in Ref. Due to Eqs. In this sense, we can understand the definition in Eq. At this point, we notice that it was already mentioned in Refs. In addition, Sonego discussed in Ref.
Here, we make the following remark. Thus, first, we have proved the inequality in Eq. The crucial steps of the proof shown above occur between Eqs.
The rearrangement above changes each of the three summands in this sum, but in doing this the value of the total sum remains unchanged. Finally, with the proof of Eq. So, the inequality in Eq. As we proved Eq.
Thus, we proved Eq. Moreover, the quantum parts of the Wyatt tensors are more easily interpreted than the quantum parts of the Kuzmenkov tensors. Fourth, one can simplify the transformation calculations by taking into account the symmetry properties in Eqs. Here, we mention that in Ref.
Andreev and Kuzmenkov compensate for their error in this approach by introducing in their QHD equations an additional inertia force. But we think that if one applies Eq. The reason for this is that the evaluation equation in Eq. So, the Wyatt pressure tensor is not only easier to interpret physically than the Kuzmenkov pressure tensor, but it is easier to apply numerically, too. In this paper, we derived the MPQHD equations in detail for an exact wave function describing an ensemble of several particle sorts.
For this task, we first derived the MPCE related to the conservation of mass for each of the particle sorts. Moreover, we derived, for each sort of particle, two different equations of motion. The first of these equations of motion is the MPEEM; it describes the temporal change of the mass flux density of the particles of the analyzed sort, and one can derive the MPEEM by applying the Ehrenfest theorem for the calculation of this temporal change.