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The Klein-Gordon equation is used to calculate the Zitterbewegung (ZB,trembling motion) of spin-zero particles in absence of fields and in thepresence of an external magnetic field. Both Hamiltonian and wave formalismsare employed to describe ZB and their results are compared. It is demonstratedthat, if one uses wave packets to represent particles, the ZB motion has adecaying behavior. It is also shown that the trembling motion is caused by aninterference of two sub-packets composed of positive and negative energy stateswhich propagate with different velocities. In the presence of a magnetic fieldthe quantization of energy spectrum results in many interband frequenciescontributing to ZB oscillations and the motion follows a collapse-revivalpattern. In the limit of non-relativistic velocities the interband ZBcomponents vanish and the motion is reduced to cyclotron oscillations. Theexact dynamics of a charged Klein-Gordon particle in the presence of a magneticfield is described on an operator level. The trembling motion of a KG particlein absence of fields is simulated using a classical model proposed by Morse andFeshbach -- it is shown that a variance of a Gaussian wave packet exhibits ZBoscillations.

Zitterbewegung of Klein-Gordon particles and its simulation by classical systems