QUANTUM MECHANICS A FUNDAMENTAL APPROACH (HB 2019) Hardcover

Quantum theory's mathematical language, using vectors and operators in complex, infinite spaces, can feel very abstract and its quantities lack obvious intuitive meaning, making it hard to grasp the formalism and quantum mechanics itself. This book aims to build intuition and provide motivation for the mathematics of quantum theory by introducing it in a simple and familiar way, starting with easily understood three-dimensional vectors and operators. Feeling secure and comfortable with the math helps readers truly appreciate and understand the concepts and structure of quantum mechanics. The book is organized into four parts. Part I briefly reviews the general characteristics of classical and quantum systems and includes a discussion of probability theory to aid in understanding its application in quantum mechanics. Part II offers a detailed exploration of the mathematical tools used in quantum mechanics. Part III presents quantum mechanics through a series of postulates, outlining six groups to describe standard quantum systems, with each postulate followed by a thorough explanation. To enhance clarity, postulates for discrete observables are presented before those for continuous observables. Part IV showcases several illustrative applications, such as harmonic and isotropic oscillators, charged particles in magnetic fields, and the Aharonov–Bohm effect. For easy navigation, definitions, theorems, examples, comments, properties, and results are clearly labeled. Various symbols and notations are used to precisely distinguish different quantities. Self-contained in both its mathematical and physical explanations, this book is accessible to a broad audience, including astrophysicists, mathematicians, and philosophers of science interested in the foundations of quantum mechanics.