  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.
