Measuring the quantum mechanical wave function

In the past few years experimenters have learned how to determine th complete quantum state of an ensemble of particles or fields which have been prepared according to some unknown procedure. Through these experiments they have answered a question posed by W. Pauli in the 1930s. The methods used involve measuring statistical distributions of a well chosen set of physical observables and using a tomographic inversion algorithm to reconstruct the Wigner function and its corresponding wave function or density math. Reconstructions have been successfully carried out in atomic, molecular, and optical physics. The development of these procedures helps to firm up the interpretation of the Schrodinger wave function.