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 [Phys. Rev. A 79, 044101 (2009)] recently pointed out that the inequality Δx=〈x2〉>λ/2 can be derived simply from the Dirac equation. Here λ=ℏ/(mc) is the Compton wavelength, x is the particle coordinate, and 〈x2〉 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.