This session explores foundational principles of wave equations, quantum mechanics, and their mathematical underpinnings. Discussions will cover wave equation derivations, quantum mechanical postulates, and mathematical frameworks such as Schrödinger's equation and the Dirac equation. Understanding the fundamentals is crucial for researchers and students alike to grasp the theoretical basis of quantum phenomena, wave propagation, and quantum states. By discussing foundational concepts, this session aims to provide a solid theoretical grounding, facilitate knowledge exchange among physicists and mathematicians, and inspire innovative research directions in quantum theory and wave equations.