Velocity vs. momentum — A new relativistic paradox

Robert F. O’Connell, Eugene Paul Wigner

Robert F. O’Connell, Eugene Paul Wigner

Francis W. Sears

S.V. Vonsovskii, Svirskii

The zitterbewegung of an electron in the case of a field with a constant nonzero scalar potential is examined. The relationship of the average velocity of the particle and its momentum is discussed, and also the relation between the energy and the scalar potential. It is shown that taking this relationship into account enables one to resolve the well-known Klein paradox in Dirac's relativistic quantum theory of the electron.

Suresh Kumar.S

Gintautas Kamuntavičius

The free relativistic particle, by definition, has to move in an inertial reference frame with uniform velocity less than the speed of light. The corresponding movement of a material quantum particle describes a wave packet, composed of matter waves—solutions of the Schr?dinger equation. The maximum of packet, corresponding to the largest probability to find the particle, has to move with the same uniform velocity, defined by the initial condition. It has been shown that the traditional definition of the quantum momentum operator i.e. taking it to correspond to the special relativity theory, relativistic momentum, cannot produce precise description of a relativistic matter particle. Different definitions are investigated and one that solves this issue is found. Obtained original expression of relativistic kinetic energy operator creates new possibilities for relativistic quantum systems theory.