A Mathematical Primer on Quantum Mechanics

Shaofan Li, Jun Li

Jonathan Dimock

Explaining the concepts in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics.

R. D. Hazeltine

We introduce the key ideas and mathematical tools central to modern discussions of collapse. We assume knowledge of basic quantum mechanics -- the Schrödinger evolution of states in Hilbert space, the Born probability rule, the Dirac formalism, and so on -- while explicating such ideas as projectors, density operators, Bell inequalities, entanglement and the Lindblad equation. In other words this work is a \emph{primer} in the simplest sense of that word: without taking a stand on the major questions, it is intended to make an enormous and growing body of research more accessible.

Franco Strocchi

Franco Strocchi

Philip L. Bowers

Quantum mechanics is one of the principle pillars of modern physics. It also remains a topic of great interest to mathematicians. Since its discovery it has inspired and been inspired by many topics within modern mathematics, including functional analysis and operator algebras, Lie groups, Lie algebras and their representations, principle bundles, distribution theory, and much more. Written with beginning graduate students in mathematics in mind, this book provides a thorough treatment of (nonrelativistic) quantum mechanics in a style that is leisurely, without the usual theorem-proof grammar of pure mathematics, while remaining mathematically honest. The author takes the time to fully develop the required mathematics and employs a consistent mathematical presentation to clarify the often-confusing notation of physics texts. Along the way the reader encounters several topics requiring more advanced mathematics than found in many discussions of the subject, making for a fascinating course in how mathematics and physics interact.