Hamiltonians and Wave Equations for Particles of Spin 0 and Spin 1/2 with Nonzero Mass

摘要

The formal mathematical structure of the truly Hamiltonian formulations of nonrelativistic and relativistic quantum mechanics is critically examined for both spin zero and spin one-half particles with nonzero mass. It is shown that the relativistic quantum mechanics can, in principle, at least be fitted into a truly covariant Hamiltonian procedure where the Hamiltonian is a Lorentz-invariant world scalar (and is the negative of one-half the rest energy of the particle, regardless of its spin). The dynamical variables associated with the translational degree of freedom of the particle (such as the position, the canonical momentum, and the velocity four-vectors of the relativistic quantum mechanics) correspond precisely to the same variables of the truly covariant formulation of relativistic classical mechanics. The mathematical structure of relativistic quantum mechanics is seen to be rather similar to that of nonrelativistic quantum mechanics for both spin zero and spin one-half particles with nonzero mass. 7 refs.