Quantum mechanical maximum velocity and wave packet deformation of high energy spinless particles

The expectation velocity of a negatively charged spinless particle is found by solving the Klein-Gordon equation for a particle moving in arbitrarily large time-independent electromagnetic fields. With the maximum expectation value of the particle velocity set equal to the velocity of light, it was found that the particle wave-packet takes on a preferred shape. It is proposed that, in order to reconcile the limitation of relativistic experimental results (which indirectly show that the particle mass increases without limit as it approaches the velocity of light), this limitation is due to the particle taking on a preferred shape. It is shown that in this Klein-Gordon quantum mechanical formulation for the case of infinitely large electromagnetic fields, the particle density may be approaching infinity as its velocity approaches the velocity of light while its mass may remain constant. It is suggested that deformation characteristics of the particle wave-packet by excessively large applied fields may be related to the necessity of renormalizing the charge and mass of the particle.