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

Grant number: 18/16631-3
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): November 01, 2018
Effective date (End): October 31, 2020
Field of knowledge:Physical Sciences and Mathematics - Physics - Atomic and Molecular Physics
Principal Investigator:Alexys Bruno Alfonso
Grantee:Murillo Rodrigues 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 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.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
SILVA, MURILLO R.; BRUNO-ALFONSO, ALEXYS. Exact and Gerchberg-Saxton solutions of the one-dimensional Pauli problem with Gaussian probability densities. Physical Review A, v. 103, n. 1, . (18/16631-3)
SILVA, MURILLO R.; BRUNO-ALFONSO, ALEXYS. Exact and Gerchberg-Saxton solutions of the one-dimensional Pauli problem with Gaussian probability densities. HYSICAL REVIEW, v. 103, n. 1, p. 9-pg., . (18/16631-3)

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