As physical science advances, theoretical simulations become increasingly reflective of realistic systems, and experimental observations become more precise and refined. Thus, going beyond the Born–Oppenheimer approximation is inevitable. This book bases its discussion of condensed matter physics on the Schrödinger equation, considering both nuclear and electronic degrees of freedom. Particular attention is given to two types of phenomena: those, such as nuclear quantum effects, for which the Born–Oppenheimer approximation, although applicable in principle, is progressively weakened in practice, and those that cannot be applied at all, such as phenomena exhibiting non-adiabatic effects. In practical systems, the full quantum nature of condensed matter, as emphasized in this book, cannot be overlooked when performing accurate simulations or measurements of material properties. This book offers state-of-the-art quantum theoretical and experimental methods, valuable for undergraduates, graduates, researchers, and industry professionals in fields such as physics, chemistry, materials science, energy, and environmental science.