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Mathematical Concepts of Quantum Mechanics
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The book gives a streamlined introduction to quantum mechanics, while describing the basic mathematical structures underpinning this discipline. Starting with an overview of the key physical experiments illustrating the origin of the physical foundations, the book proceeds to a description of the basic notions of quantum mechanics and their mathematical content.
It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The topics presented include spectral theory, many-body theory, positive temperatures, path integrals and quasiclassical asymptotics, the theory of resonances, an introduction to quantum field theory and the theory of radiation.
The book can serve as a text for an intermediate course in quantum mechanics, or a more advanced topics course.
It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The topics presented include spectral theory, many-body theory, positive temperatures, path integrals and quasiclassical asymptotics, the theory of resonances, an introduction to quantum field theory and the theory of radiation.
The book can serve as a text for an intermediate course in quantum mechanics, or a more advanced topics course.
The book gives a streamlined introduction to quantum mechanics and describes the basic mathematical structures underpinning it. From the reviews: "This book is an introduction to the mathematics of quantum mechanics....The strength of the book is where it shows how the mathematical treatment of quantum mechanics brings insights to physics....It will be useful to the experienced reader as a guide to the impressive recent advances in mathematical quantum mechanics." --SIAM REVIEW