Self-action in a system of elementary particles

Potential energy in Schrödinger equation does not contain the potential energy of the interaction of the elementary particle considered with the field, created by this same particle. If someone will average quantum mechanically Schrödinger equation, he/she will see that the total energy does not contain the particle potential energy, as it is not present in Schrödinger equation. Hence in quantum mechanics action of the elementary particle on itself, that is a self-action, should not be taken into account. It is a well known fact1. Thus, a charged elementary particle does not possess an electric potential energy in quantum mechanics, as it is not present in Schrödinger equation. From this follows, in particular, that the electrostatic energy of the charges in a hydrogen atom in a ground state consists of the negative interaction energy of the negatively charged electron with positively charged proton only2. In classical electrostatics electric potential energy is always positive, as it is proportional to the electrostatic field in square. In a positronium (a hydrogen type atom, which consists of a positron and electron) the masses of both particles are equal. The charges of the particles are of the same value, but of the opposite signs. That is why the wave functions of both particles are identical. From this follows that in a positronium in a ground state there is no local electric charge, no electric field, but there is negative electrostatic energy2. Since Schrödinger equation was introduced in 1926, it is a well known fact that self-action in quantum mechanics should not be taken into account. It is a mainstream opinion, not an alternative one. In particular, when performing calculations in many-body theory3,4, self-action of any electron was never taken into account. Calculated spectra are in a very good agreement with experiment3,4. The simplest example is the atom of hydrogen spectra. They were also never calculated, taking into account self-action of the electron in a hydrogen atom. So, in2 there is no one single result of Y. Kornyushin, as well as it contains no one new result at all. All what is written here and in2 was very well known more than 80 years ago. Today the concepts discussed here are as important as they were 80 years ago and should be studied well.

References

1. Landau, L. D., and Lifshitz, E. M., 1987, Quantum Mechanics (Oxford: Pergamon).

2. Y. Kornyushin, 2009, http://arxiv.org/abs/0806.3828v5.

3. Hartree, D., 1957, The Calculation of Atomic Structure (New York: WileyInterscience).

4. Fock, V. A., 1930 Z. Phys. 61 126.