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.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
