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Quantum mechanics differential equations are based on the de Broglie wavelength assigned to a particle. The fundamental equation of quantum mechanics, namely the Schrödinger equation, describes the movement of a point-like particle. This paper presents the effect on quantum mechanics differential equations when replacing the de Broglie wavelength by a relation between the focal radius of a particle and its total relativistic energy. This relation results from a theoretical work from the author about the interaction of particles, where particles are modeled as emitting and absorbing continuously fundamental particles with longitudinal and transversal angular momentum. The laws of interaction are mathematically formulated in that way, that the basic laws of physics (Coulomb, Ampere, Lorentz, Maxwell, Gravitation, bending and interference of light and particles), can be deduced from them. The main effect on quantum mechanics is the change of the pairs of canonical conjugated variables that are linked by the uncertainty principle of Heisenberg, namely, to the pairs energy-space and momentum-time. This has the consequence on relativistic and non-relativistic operators in that they are reversed respect to time and space derivations compared with standard theory. The accordance of the proposed theory with the correspondence principle of quantum mechanics is proven in that the time independent differential equation from Schroedinger, deduced from the wave package constructed with the de Broglie wavelength, can be also derived from the wave package constructed with the foca-radius-energy relation. Solutions of the new differential equation for the potential pot, the harmonic oscillator and the hydrogen atom are presented and compared with the solutions of the Schroedinger differential equation

This paper presents the mechanism of gravitation based on an approach where the energy of an electron or positron is radially distributed in space from a focal point to infinite. The energy is stored in fundamental particles (FPs) that move continuously through the focal point in space, point where classically the energy of a subatomic particle is thought to be concentrated. Electrons and positrons that have migrated slowly out of the core of their nuclei are reintegrated with high speed generating a field that is responsible for two components of the gravitation force, according if the reintegration is parallel to the distance between the gravitating bodies or perpendicular. For sub-galactic distances the component that is inverse proportional to the square distance predominates, while for galactic distances the component that is inverse proportional to the distance is predominant explaining the flattening of the velocity curve of galaxies without the need of black matter.

This work presents a relativistic mathematical model for basic subatomic particles (BSPs) like electrons, positrons and neutrinos, model that is based on fundamental particles that are continuously emitted and absorbed by the subatomic particles. Subatomic particles interact via the longitudinal and transversal angular momentum of their fundamental particles, angular momentum that are proportional to the energy of the subatomic particles. The rules of interaction between the longitudinal and transversal angular momentum of fundamental particles are specified and the corresponding equations for the calculations of the linear momentum between subatomic particles are presented. From the model results that the radius of a subatomic particle is inverse proportional to its energy and, that the incremental time to generate the force out of linear momentum is quantized. All known forces are derived as rotors from one vector field generated by the longitudinal and transversal angular momentum of the fundamental particles. The equation of the linear momentum between two static BSPs is analyzed in detail to show why protons in an atomic nucleus coexist, how gravitation is generated and why heavy atomic nuclei radiate. The mechanism of elastic and destructive scattering of particles, based on the interactions between fundamental particles, is described. A classification of BSPs with light speed is presented and the photon introduced as a sequence of BSPs. Based on the quantification of the irradiated energy of BSPs, the Bragg equation, the Stern Gerlach bending and the flattening of galaxies' rotation curve are derived, without making use respectively of the wave-particle, the magnetic spin moment and dark matter, thus introducing a different physical interpretation of the underlying phenomenon. The two states of the spin of BSPs is replaced by the pair building of two types of BSPs, namely the accelerating and decelerating BSPs. (For full version see related website)