This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. The mathematical structure of QM is formulated in terms of the C*algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables, for a general physical system. The Diracvon Neumann axioms are then derived. The description of states and observables as Hilbert space vectors and operators follows from the GNS and GelfandNaimark Theorems. The experimental existence of complementary observables for atomic systems is shown to imply the noncommutativity of the observable algebra, the distinctive feature of QM for finite degrees of freedom, the Weyl algebra codifies the experimental complementarity of position and momentum (Heisenberg commutation relations) and Schrodinger QM follows from the von Neumann uniqueness theorem.The existence problem of the dynamics is related to the selfadjointness of the Hamiltonian and solved by the KatoRellich conditions on the potential, which also guarantee quantum stability for classically unboundedbelow Hamiltonians. 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 (FeynmanKac formula), to the formulation in terms of ground state correlations (the quantum mechanical analog of the Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle is discussed in detail, as an example of the interplay between topology and functional integral, leading to the emergence of superselection rules and sectors.
About F. Strocchi
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Author  :  F. Strocchi 
Publisher  :  World Scientific Publishing Co Pte Ltd 
Data Published  :  01 January 2020 
ISBN  :  9812835229 
EAN  :  9789812835222 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  180 pages 
Age +  :  18 years 
Language  :  English 
Rating  : 
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