Year: 2013 Pages: 7

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