Quantum Mechanics: A Mathematical

Starting from basic principles, the book systematically covers both Heisenberg and Schrödinger realizations of quantum mechanics (in this order). The material traditionally presented in quantum textbooks is illustrated with applications which are (or will become) cornerstones of future technologies. The emphasis in the matrix formulation focus the attention on the spin, the most important quantum observable, and paves the way to chapters on quantum information (including crytography, teleportation and computation), on recent tests of quantum physics and on decoherence. Additions and changes found in the second edition include; a more friendly presentation to Hilbert spaces; more practical applications e.g. scanning tunneling microscope (potential barrier); quantum dots (single-particle states in semiconductors); lasers and masers (induced emission); real experiments that have recently provided a qualitative change in the foundations of quantum physics; and an outline of the density matrix formalism as applied to a simple model of decoherence.

This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined.

Reviews from the First Edition:
"An excellent text … The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)

The first fifteen chapters of these lectures (omitting four to six chapters each year) cover a one term course taken by a mixed group of senior undergraduate and junior graduate students specializing either in mathematics or physics. Typically, the mathematics students have some background in advanced anal­ ysis, while the physics students have had introductory quantum mechanics. To satisfy such a disparate audience, we decided to select material which is interesting from the viewpoint of modern theoretical physics, and which illustrates an interplay of ideas from various fields of mathematics such as operator theory, probability, differential equations, and differential geometry.