Zitterbewegung and the Klein paradox for spin-zero particles

The Hamiltonian form of the Klein-Gordon equation is used to study the Zitterbewegung of spin-zero particles. It is shown that the time dependence of the velocity and position operators in the Heisenberg picture is formally the same as that of a spin-1/2 particle. It is also shown that the Zitterbewegung is the result of the interference between positive and negative energy states. A representation-free expression is found for the mean position operator. This operator is free from Zitterbewegung. The Klein-Gordon equation is solved with an electrostatic potential originally used by Sauter in his investigation of the Klein paradox for spin-1/2 particles. It is shown that the transmission to states with negative kinetic energy is very small when the electric field is weak.