Motion of Charged Particles in a Homogeneous Magnetic Field

A general and simple method is presented to calculate the eigenvalues of the eigenequation for the theory of a particle with any spin with anomalous-magnetic-moment coupling moving in a homogeneous magnetic field. The eigenvalues of the spin-$\frac{1}{2}$ and spin-1 systems are obtained specifically. This method of approach does not require an explicit solution of the eigenfunction equation. Different spin-1 theories (vector theory, multispinor theory, and 6-component theory) are discussed, and in the case of no anomalous-magnetic-moment coupling terms, all these theories predict the same eigenvalues. Furthermore, by requiring that the energy eigenvalues be positive definite, we show that the vector spin-1 theory is consistent only when no anomalous-magnetic-moment coupling terms exist.