Position Operators for Systems Exhibiting the Special Relativistic Relation Between Momentum and Velocity

Abstract

We have previously shown [1] that if the position operator is defined as in ref. [21, the movement of the mean position of a free particle obeys the classical equation υ = P/P ₀ where P₀ is the total energy, including the rest mass. Conversely, it will be demonstrated here that the validity of this equation implies that, for spinless particles, the position operator is that of ref. [2]. For spin 1/2 particles, however, another choice is also possible (eq. (7)). The corresponding value of the orbital angular momentum in the latter case is unity, whereas for the state of ref. [2] it is zero.