Mathematical Physics and the Study of Complex Quantum Systems - Ana Uzla Batubara; Zainab Ali; Arnes Yuli Vandika (Yayasan Adra Karima Hubbi, 2024)
The study of complex quantum systems is a fundamental aspect of modern physics, providing insights into the behavior of matter at microscopic scales. Mathematical physics plays a crucial role in developing the theoretical frameworks necessary for understanding these systems, yet challenges remain in applying these concepts to real-world scenarios. This research aims to investigate the application of mathematical techniques in analyzing complex quantum systems. The focus is on identifying effective mathematical models and methods that can enhance our understanding of quantum phenomena. A comprehensive literature review was conducted, analyzing various mathematical approaches utilized in quantum mechanics, including perturbation theory, group theory, and numerical simulations. Case studies were examined to illustrate the successful application of these methods in real-world quantum systems. Findings indicate that advanced mathematical techniques significantly improve the modeling and analysis of complex quantum systems. The application of perturbation theory and numerical simulations provided deeper insights into system behaviors, while group theory facilitated a better understanding of symmetry properties. This research highlights the indispensable role of mathematical physics in the study of complex quantum systems. By emphasizing the integration of mathematical techniques, the study contributes to the advancement of theoretical physics and offers pathways for future research in quantum mechanics.