Klein–Gordon equation for electrically charged particles with new energy-momentum operator

Abstract

We address the Klein–Gordon equation for a spinless charged particle in the presence of an electromagnetic (EM) field, and focus on its known shortcoming, related to the existence of solutions with a negative probability density. We disclose a principal way to overcome this shortcoming, using our recent results obtained in the analysis of quantum phase effects for charges and dipoles, which prove the need to abandon the customary definition of the momentum operator for a charged particle in an EM field through its canonical momentum, and to adopt the more general definition of this operator through the sum of mechanical and EM momenta for the system ‘charged particle in an EM field’. We show that the application of the new energy-momentum operator to the Klein–Gordon equation actually eliminates solutions with negative probability density. Some implications of the obtained results are discussed.