A realistic interpretation of the density matrix II: The non-relativistic case

Abstract

The interpretation proposed in quant-ph/9812011 is extended to the general case of a non-relativistic particle moving in an arbitrary external potential. It is shown that, even in this general case, "particle" solutions exist which do not spread out with time, and remain well localized around their center of mass; it is postulated that these are the only solutions which represent individual physical particles. As a consequence two basic principles of standard QM, namely the superposition principle and the wave-function collapse, are shown to have no ontological meaning. Three simple applications of our approach are then examined: the free particle, the linear harmonic oscillator and the delta barrier potential; the corresponding "particle" solutions are explicitly shown. Finally, it is argued that the persisting confusion about the meaning of the wave-function (does it represent an individual particle or a statistical ensemble?) calls for a non-linear extension of the Schroedinger equation.