OBSERVATION OF MOVING WAVE-PACKETS REVEALS THEIR QUANTUM STATE

We show how to infer the quantum state of a wave packet from position probability distributions measured during the packet's motion in an ar bitrary potential. We assume a nonrelativistic one-dimensional or radi al wave packet. Temporal Fourier transformation and spatial sampling w ith respect to a newly found set of functions project the density-matr ix elements out of the probability distributions. The sampling functio ns are derivatives of products of regular and irregular wave functions . We note that the ability to infer quantum states in this way depends on the structure of the Schrodinger equation.