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An Introduction to the Mathematical Structure of Quantum Mechanics: A Short Course for Mathematicians (Advanced Series in Mathmatical Physics) [Hardcover]

By F. Strocchi (Author)
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Item description for An Introduction to the Mathematical Structure of Quantum Mechanics: A Short Course for Mathematicians (Advanced Series in Mathmatical Physics) by F. Strocchi...

This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. Rather than starting from the Dirac--Von Neumann axioms, the book offers a short presentation of the mathematical structure of QM using the C*-algebraic structure of the observable based on the operational definition of measurements and the duality between states and observables. The description of states and observables as Hilbert space vectors and operators is then derived from the GNS and Gelfand--Naimark Theorems. For finite degrees of freedom, the Weyl algebra codifies the experimental limitations on the measurements of position and momentum (Heisenberg uncertainty relations) and Schroedinger QM follows from the von Neumann uniqueness theorem. The existence problem of the dynamics is related to the self-adjointness of the differential operator describing the Hamiltonian and solved by the Rellich--Kato theorems. Examples are discussed which include the explanation of the discreteness of the atomic spectra. Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman--Kac formula), the formulation in terms of ground state correlations (Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle as an example of the interplay between topology and functional integral is also discussed in detail.



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Item Specifications...


Studio: World Scientific Publishing Company
Pages   460
Est. Packaging Dimensions:   Length: 8.8" Width: 6" Height: 0.7"
Weight:   0.75 lbs.
Binding  Hardcover
Release Date   Nov 2, 2005
Publisher   World Scientific Publishing Company
ISBN  9812564314  
ISBN13  9789812564313  


Availability  0 units.


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Product Categories

1Books > Special Features > New & Used Textbooks
2Books > Subjects > Professional & Technical > Professional Science > Physics > Mathematical Physics
3Books > Subjects > Professional & Technical > Professional Science > Physics > Quantum Theory
4Books > Subjects > Science > General
5Books > Subjects > Science > Mathematics > General
6Books > Subjects > Science > Physics > General
7Books > Subjects > Science > Physics > Mathematical Physics
8Books > Subjects > Science > Physics > Quantum Theory



Reviews - What do customers think about An Introduction to the Mathematical Structure of Quantum Mechanics: A Short Course for Mathematicians (Advanced Series in Mathmatical Physics)?

Artur O. Lopes  Apr 28, 2007
Excellent mathematical exposition. A very clear description of the basic
ideas and results of Quantum Mechanics using (from the beginning of the book) the point of view of C*-Algebras.
 

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