Minimum uncertainty wave packet in relativistic quantum mechanics

In nonrelativistic quantum mechanics in one dimension a wave packet can be constructed for which the minimum uncertainty relation for position and momentum, ΔxΔp=ℏ/2, holds exactly. The wave function of the wave packet is Gaussian and satisfies the Schrödinger equation for a harmonic oscillator potential. We illustrate a similar situation in relativistic quantum mechanics for the one-dimensional Dirac equation.