Operators in Hilbert Spaces and Applications to Quantum Mechanics

• Grant number: 22/09938-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2022
• End date: September 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Márcia Cristina Anderson Braz Federson
• Grantee: Sergio Noboru Yuzuka
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The objective of this project is to provide the candidate with the opportunity to deepen their studies of the mathematical tools used in Quantum Mechanics. Thus, our proposal is that he investigates the theory of operators in Hilbert spaces and its applications to Quantum Mechanics. As a secondary objective, we believe that it is pertinent and necessary for the candidate to produce notes or a handout on the subject, with all the appropriate mathematical detail so that any other student, at the end of an undergraduate course in the area of exact sciences, can follow the text and understand the topics involved without much difficulty.