Scattering experiments for measuring the wave function of a single system

We suggest scattering experiments allowing the measurement of the complete wave function even when only one quantum system (rather than an ensemble) is available. Such scattering experiments require massive, slow, projectiles with kinetic energies lower than the first excitation of the system in question. The accidental absence of optimal projectiles of this type may be one of the reasons why this conceptual possibility was not realized before.