Quantum mechanics on curved surfaces

• Grant number: 18/07880-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2018
• End date: July 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Alberto Vazquez Saa
• Grantee: Vinicius Maciel e Souza
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 13/09357-9 - Physics and geometry of spacetime, AP.TEM

Abstract

This project consists in an introduction to the Canonical Quantization procedure through an explicit concrete problem: the quantum description of the motion of a particle, under the action of an external potential or not, constrained to move on a smooth surface of $\mathbb{R}^3$. By describing the classical associated problem using generalized coordinates adapted to a parametrization of the surface, some severe ordering ambiguities in the definition of the momentum operator arise. We expect that the analysis of this problem will provide to the student a good opportunity to learn about certain subtle quantization issues, among them the van Hove theorem and the role played by symmetries and anomalies in quantum systems. (AU)