Conversion of the Non-relativistic Schrödinger Equation: Into a Class Relativistic Equations

Until now, it has been generally believed that the Schrödinger equation belongs to the class of non-relativistic equations; that is, the modeling of an elementary particle by means of this equation was considered possible only if the velocity ¿ of the particle was many times than the speed of light c in a vacuum. However, the present monograph demonstrates that the velocity of a particle described by the Schrödinger equation may, in fact, be equal to the speed of light. This circumstance makes it possible to assert that the Schrödinger equation is a universal equation, since it can be used to model particles possessing arbitrary velocities. Consequently, the Schrödinger equation belongs both to the non-relativistic and the relativistic classes of equations; everything depends on the mathematical apparatus employed in solving this equation.The transfer of the Schrödinger equation into the class of relativistic equations became possible through the derivation of an antiparticle model, i.e., a model of antimatter. In this case, a process of annihilation between a particle and an antiparticle occurs, resulting in a particle whose rest mass is equal to zero.