QUANTUM MATHEMATICS AND PHYSICS: STUDYING MATHEMATICAL FOUNDATIONS AND APPLICATIONS

Abstract

Quantum mechanics and quantum physics have revolutionized our understanding of the fundamental nature of reality. At the core of this revolution lies quantum mathematics, which provides the mathematical foundation for describing the motion of particles at microscopic scales. This article explores the fundamental mathematical structures of quantum mechanics, including Hilbert spaces, operators, and wave functions, as well as their applications in modeling physical systems. The research also examines how quantum physics contrasts with classical physics concepts and offers new insights into topics such as quantum entanglement, superposition, and quantum computing. By analyzing the mathematical foundations of quantum theories, the article aims to shed light on the intersection of mathematics and physics, offering a deeper understanding of how mathematical formulas help predict and explain quantum phenomena. Furthermore, it discusses the potential implications of quantum mathematics in emerging fields such as quantum computing and cryptography.