The Heisenberg Uncertainty Principle and its Applications

• Grant number: 23/15045-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2024
• End date: December 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Physics - Atomic and Molecular Physics
• Principal Investigator: Alexys Bruno Alfonso
• Grantee: Karen Fernanda Pagnoni
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

The mathematical formalism of Quantum Mechanics are near to celebrate a century of development, with a hilt impact on natural science and the high technology. The Heisenberg uncertainty principle is the most popular topic of this theory. Many High School and Modern Physics text-books have discussions and applications about the uncertainty relations between position and linear momentum, considering its apparent mathematical simplicity. Estimates about the position, linear momentum, and energy of particles are often proposed. In the case of the Hydrogen atom, some estimates are poorly justified, due to insufficient detailing of the mathematical treatment. Although this problem has been highlighted in specialized literature, the issue found in classic texts (e.g., Bohm, Feynman, Eisberg) continues to be reproduced (e.g., Nussenzveig). This Research Project aims to contribute to a more complete understanding of the Heisenberg uncertainty principle and its applications. Specifically, the Research aims to discuss the principle potential for making quantitative estimates, as well as the mathematical precautions to consider.