Authors: Jérémy Kerneis
We use three postulates P1, P2a/b and P3 : Combining P1 and P2a with "Sommerfeld's quantum rules"; correspond to the original quan- tum theory of Hydrogen, which produces the correct relativistic energy levels for atoms (Sommerfeld's and Dirac's theories of matter produces the same energy levels, and Schrodinger's theory produces the approximation of those energy levels). P3 can be found in Schrodinger's famous paper introducing his equation, P3 being his first assumption (a second assumption, suppressed here, is required to deduce his equation). P3 implies that the wavefunction solution of both Schrodinger's and Klein-Gordon's equations in the non interacting case while, in the interacting case, it immediatly implies "Sommerfeld's quantum rules" : P1, P2a, and P3 then produce the correct relativistic energy levels of atoms, and we check that the required degeneracy is justied by pure deduction, without any other assumption (Schrodinger's theory only justies one half of the degeneracy). We observe that the introduction of an interaction in P1 is equivalent to a modication of the metric inside the wavefunction in P3, such that the equation of motion of a system can be deduced with two dierent methods, with or without the metric. Replacing the electromagnetic potential P2a by the suggested gravitationnal potential P2b, the equation of motion (deduced in two ways) is equivalent to the equation of motion of General Relativity in the low field approximation (with accuracy 10-6 at the surface of the Sun). We have no coordinate singularity inside the metric. Other motions can be obtained by modifying P2b, the theory is adaptable. First of all, we discuss classical Kepler problems (Newtonian motion of the Earth around the Sun), explain the link between Kelpler law of periods (1619) and Plank's law (1900) and observe the links between all historical models of atoms (Bohr, Sommerfeld, Pauli, Schrodinger, Dirac, Fock). This being done, we introduce P1, P2a/b, and P3 to then describe electromagnetism and gravitation in the same formalism.
Comments: 21 Pages.
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