TITLE:
Quantum Mechanics and Special Relativity: The Origin of Momentum Operator
AUTHORS:
Gintautas P. Kamuntavičius
KEYWORDS:
Special Relativity, Quantum Mechanics, Relativistic Wave Equations
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.10,
October
24,
2018
ABSTRACT: 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.