Introduction

When, in 1926, Schrödinger came to publish his non-relativistic wave equation (Schrödinger, 1926), namely the equation we discretized in the previous chapter, he had previously considered a special-relativistic wave equation, but discarded it on account of some of its properties, which he believed were unphysical. In particular, that relativistic equation has a conserved current density that cannot be interpreted as a classical probability current density because it can take on negative values, something that a true probability density would not do. If Schrödinger had been aware of antiparticles, which were discovered several years later, it is conceivable that he would have persisted with that relativistic wave equation. The equation he discarded is sometimes referred to as the Schrödinger–Fock–Klein–Gordon equation, but more commonly is known as just the Klein–Gordon (K–G) equation.

The significance of Schrödinger's rejection of the K–G equation lies in his decision to forgo Lorentz covariance in favour of an intuitive, albeit non-relativistic, interpretation of the wave equation that now bears his name. Schrödinger's nonrelativistic wave equation was extraordinarily successful when applied to atomic physics, which greatly contributed to the rise of quantum physics.

Within two years, however, the situation was dramatically restored in favour of special relativity. In 1928 Dirac published his famous Lorentz covariant wave equation for the electron (Dirac, 1928).