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An Introduction to Hilbert Space and Quantum Logic (Problem Books in Mathematics)


An Introduction to Hilbert Space and Quantum Logic (Problem Books in Mathematics) Cover


Synopses & Reviews

Publisher Comments:

Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.

Table of Contents

Contents: Experiments, Measure, and Integration: Measures. Integration. Hilbert Space Basics.- The Logic of Nonclassical Physics: Manuals of Experiments and Weights. Logics and State Functions. Subspaces in Hilbert Space.- Maps on Hilbert Spaces: Linear Functionals and Function Spaces. Projection Operators and the Projection Logic.- State Space and Gleason's Theorem: The Geometry of State Space. Gleason's Theorem.- Spectrality: Finite Dimensional Spaces, The Spectral Resolution Theorem. Infinite Dimensional Spaces, The Spectral Theorem.- The Hilbert Space Model for Quantum Mechanics and the EPR Dilemma: A Brief History of Quantum Mechanics. A Hilbert Space Model for Quantum Mechanics. The EPR Experiment and the Challenge of the Realists.- Index of Definitions.

Product Details

Cohen, David W.
Cohen, David W.
Mathematics - Advanced
Mathematical Physics
Theoretical, Mathematical and Computational Physics
Edition Description:
Softcover reprint of the original 1st ed. 1989
Problem Books in Mathematics
Publication Date:
235 x 155 mm 259 gr

Related Subjects

Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Physics » General
Science and Mathematics » Physics » Math

An Introduction to Hilbert Space and Quantum Logic (Problem Books in Mathematics) New Trade Paper
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Product details 161 pages Springer - English 9781461388432 Reviews:
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