Quantum Theory / Particle Physics
September 22, 2017
Fundamental equations of relativistic quantum hydrodynamics, free particles and photons, Casimir energy, total energy of a particle and a bound photon wave
In the present paper we solve the relativistic quantum hydrodynamic fundamental equations for free particles and photons in the ground state. We obtain as solution spherical harmonics and spherical Bessel functions. According to our model conception, the definition domain of the ground state ... consists of two intervals: We put the free photons in the ground state 1. into the density distribution of a free particle in the interval ... and 2. as a bound photon wave in the interval ... and calculate thereby the corresponding Casimir energies using the Euler-MacLaurin sum formula. Under the condition of the hydrodynamic equilibrium between the attractive and repulsive Casimir forces, we deduce the total energy (= the photon energy) of the free particle and the bound photon wave. Numerical calculations for the neutron indicate that the novel model conception of two intervals in one and the same ground state is overall a consistent relativistic quantum hydrodynamic description.