Confinement limit of the Dirac particle in one dimension

For a particle of mass m that obeys the time-independent Dirac equation in one dimension with a symmetric potential, Unanyan et al. [Phys. Rev. A 79, 044101 (2009)] recently pointed out that the inequality Δx=√(>λ/2 can be derived simply from the Dirac equation. Here λ=(ℎ/2π)/(mc) is the Compton wavelength, x is the particle coordinate, and is the expectation value of x2. We conjecture that a new, more stringent limit Δx≥λ/√(2) holds for any symmetric potential. We present a model analysis on which the conjecture is based.