Generalization of the Gerchberg-Saxton Algorithm to Reconstruct the Quantum States of a Particle

• Grant number: 24/04312-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2024
• End date: May 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Physics - Atomic and Molecular Physics
• Principal Investigator: Alexys Bruno Alfonso
• Grantee: Felipe Andrade Ferreira da Silva
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

A central problem in Quantum Mechanics is the search for experimental information on the wavefunction. In 1933, Pauli commented on whether that function can be determined, provided one knows the probability densities for position and linear momentum of a particle. From the mathematical viewpoint, this is called as the phase-retrieval problem. The proposal aims to contribute for the physical, mathematical and computational treatments of the problem. The Gershberg-Saxton algorithm retrieves the phase by successive approximations. Usually, the problem has various solutions and the limit solution depends on the initial approximation. The Project will involve a generalization of the Gershberg-Saxton algorithm. Appropriate weights will be introduced to lower round-off errors in the phase updates. The computational convergence and mathematical and physical consistency of the results will be addressed, by considering several pairs of position and momentum probability distributions.