A Link Between Relativistic Rest Energy and Fractionary Momentum Operators of Order 1/2

Abstract

The solution of a causal fractionary wave equation in an infinite potential well was obtained. First, the so-called "free particle" case was solved, giving as normalizable solutions a superposition of damped oscillations similar to a wave packet. From this results, the infinite potential well case was then solved. The damping coefficient of the equation obtained was matched with the exponent appearing in the Yucawa potential or "screened" Coulomb potential. When this matching was forced, the particle aquires an offset energy of E = mc^2/2 which then can be increased by each energy level. The expontential damping of the wave solutions in the box was found to be closely related with the radius of the proton when the particle has a mass equal to the mass of the proton. Lastly the fractionary wave equation was expressed in spherical coordinates and remains to be solved through analytical or numerical methods.