Physical Interpretation of the Solutions to the Dirac Equation

Bernard H. Lavenda

Toyoki Koga

Patrick Vaudon

Dirac equation is one of the fundamental equations of quantum mechanics, but the interpretation of its solutions in terms of spinors is very abstract. It is proposed in this paper to show that some electromagnetic solutions exist in terms of standing waves. We shall exhibit explicit solutions as standing modes of a rectangular electromagnetic cavity. We conclude by proposing a physical interpretation of the new terms which appear in the Dirac solution.

S. M. Neamtan

The usual choice of an orthogonal set of four plane-wave solutions of the free-particle Dirac equation does not lend itself readily to direct and complete physical interpretation except in low-energy approximation. A different choice of solutions can be made which yields a direct physical interpretation at all energies. Besides the separation of positive and negative energy states there is a further separation of states for which the spin is respectively parallel or antiparallel to the direction of the momentum vector.

Khinlay Win, A. Petridis

J. Iliopoulos, Theodore N. Tomaras

Abstract The Klein–Gordon and the Dirac equations are studied as candidates for a relativistic generalisation of the Schrödinger equation. We show that the first is unacceptable because it admits solutions with arbitrarily large negative energy and has no conserved current with positive definite probability density. The Dirac equation on the other hand does have a physically acceptable conserved current, but it too suffers from the presence of negative energy solutions. We show that the latter can be interpreted as describing anti-particles. In either case there is no fully consistent interpretation as a single-particle wave equation and we are led to a formalism admitting an infinite number of degrees of freedom, that is a quantum field theory. We can still use the Dirac equation at low energies when the effects of anti-particles are negligible and we study applications in atomic physics.