PROBABILITY BACKFLOW FOR A DIRAC PARTICLE

The phenomenon of probability backflow, previously quantified for a fr ee nonrelativistic particle, is considered for a free particle obeying Dirac's equation. It is known that probability backflow can occur in the opposite direction to the momentum; that is to say, there exist po sitive-energy states in which the particle certainly has a positive mo mentum in a given direction, but for which the component of the probab ility flux vector in that direction is negative. It is shown thar the maximum possible amount of probability that can flow ''backwards,'' ov er a given time interval of duration T, depends on the dimensionless p arameter epsilon = root 4h/mc(2)T, where m is the mass of the particle and c is the speed of light. At epsilon = 0, the nonrelativistic valu e of approximately 0.039 for this maximum is recovered. Numerical stud ies suggest that the maximum decreases monotonically as epsilon increa ses from 0, and show that it depends on the size of m, h, and T, unlik e the nonrelativistic case.