SINGLE-PARTICLE INTERPRETATION OF THE DIRAC EQUATION WITHIN AN INFINITE SET OF PICTURES.

Г. А. Зайцев

Mitchel Weissbluth

R. Gerritsma, Gerhard Kirchmair, F. Zähringer +3 more

R. JAGANATHAN

It has been found that quantum corrections can substantially affect the classical results of tracking for trajectories close to the separatrix. Hence the development of a basic formalism for obtaining the quantum maps for any particle beam optical system is called for. To this end, it is observed that several aspects of quantum maps for the beam optics of spin-1/2 particles can be studied, at the level of single particle dynamics, using the proper formalism based on the Dirac equation.

K.H. Tzou, 浙江大学物理系

In this paper, as suggested by the classical canonical equations, a new set of the corresponding relativistic equations is set up. Therefrom a relativistic form of Heisenberg's equation is deduced. The rclalivistic Hamiltonian system of a particle according to the formulation here established has been fully discussed and by following it, however, Diracs equation appears naturally as a necessary form of relativistic wave equation tor electron in quantum mechanics. The process of taking square root in Dirac's theory is seen to have its classical analogy. Finally, some applications of the relativistic Heisenberg's equation to Dirac's theory have been discussed and it has thereby been pointed out that this equation brings some quantities to being more symmetrical in the relativity sense and also some more general than those the non-relativistic equation can introduce.