The phase problem in quantum mechanics: wave function retrieval from probability densities

Abstract

A central problem in Quantum Mechanics is the search for experimental information on the wavefunction. In 1933, Pauli commented on whether it can be done, provided one knows the probability densities for position and linear momentum of a particle. From the mathematical viewpoint, this is called as the phase problem. The proposal aims physical, mathematical and computational treatments of the problem. First, computational codes based on the Gershberg-Saxton algorithm will be developed. Tests for several probability densities of position and linear momentum will be done. The algorithms will be modified, in order to improve convergence and accuracy, as well as to assess existence and uniqueness of solutions for the phase problem. The proposed research will find applications in quantum tomography and quantum computing.