  Quantum particles in a potential are described by classical statistical
probabilities. We formulate a basic time evolution law for the probability
distribution of classical position and momentum such that all known quantum
phenomena follow, including interference or tunneling. The appropriate quantum
observables for position and momentum contain a statistical part which reflects
the roughness of the probability distribution. "Zwitters" realize a continuous
interpolation between quantum and classical particles. Such objects may provide
for an effective one-particle description of classical or quantum collective
states as droplets of a liquid, macromolecules or a Bose-Einstein condensate.
They may also be used for quantitative fundamental tests of quantum mechanics.
We show that the ground state for zwitters has no longer a sharp energy. This
feature permits to put quantitative experimental bounds on a small parameter
for possible deviations from quantum mechanics.
