Quantum Mechanics. A Mathematical Introduction

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline.

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline.

Learn the fundamentals of quantum physics and test your knowledge with 100+ practice problems.

This course-based primer offers readers a concise introduction to the description of quantum mechanical systems with infinitely many degrees of freedom – and quantum spin systems in particular – using the operator algebraic approach. Here, the observables are modeled using elements of some operator algebra, usually a C*-algebra. This text introduces readers to the framework and the necessary mathematical tools without assuming much mathematical background, making it more accessible than advanced monographs.

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. A comprehensive bibliography and index round out the work.

The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. Furthermore, such a rigorous mathematical foundation leads to a more profound insight into the nature of quantum mechanics. This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics.

This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory.