Historically, nonclassical physics developed in three stages. First came a collection ofad 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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
1. Experiments, Measure, and Integration.- A. Measures.- Experiments and weight functions, expected value of a weight function, measures, Lebesgue measure, signed measures, complex measures, measurable functions, almost everywhere equality..- B. Integration.- Simple functions, simple integrals, general integrals, Lebesgue integrals, properties of integrals, expected values as integrals, complex integrals..- 2. Hilbert Space Basics.- Inner product space, norm, orthogonality, Pythagorean theorem, Bessel and Cauchy-Schwarz and triangle inequalities, Cauchy sequences, convergence in norm, completeness, Hilbert space, summability, bases, dimension..- 3. The Logic of Nonclassical Physics.- A. Manuals of Experiments and Weights.- Manuals, outcomes, events, orthogonality, refinements, compatibility, weights on manuals, electron spin, dispersion-free weights, uncertainty..- B. Logics and State Functions.- Implication in manuals, logical equivalence, operational logic, implication and orthocomplementation in the logic, lattices, general logics (quantum logics), propositions, compatibility, states on logics, pure states, epistemic and ontological uncertainty..- 4. Subspaces in Hilbert Space.- Linear manifolds, closure, subspaces, spans, orthogonal complements, the subspace logic, finite projection theorem, compatibility of subspaces..- 5. Maps on Hilbert Spaces.- A. Linear Functional and Function Spaces.- Linear maps, continuity, boundedness, linear functional, Riesz representation theorem, dual spaces, adjoints, Hermitian operators..- B. Projection Operators and the Projection Logic.- Projection operators, summability of operators, the projection logic, compatibility and commutativity..- 6. State Space and Gleason’s Theorem.- A. The Geometry of State Space.- State space, convexity, faces, extreme points, properties, detectability, pure states, observables, spectrum, expected values, exposed faces..- B. Gleason’s Theorem.- Vector state, mixture, resolution of an operator into projection operators, expected values of operators, Gleason’s theorem..- 7. Spectrality.- A. Finite Dimensional Spaces, the Spectral Resolution Theorem.- Eigenvalues, point spectrum, eigenspaces, diagonalization, the spectral resolution theorem..- B. Infinite Dimensional Spaces, the Spectral Theorem.- Spectral values, spectral measures, the spectral theorem, functions of operators, commutativity and functional relationships between operators, commutativity and compatibility of operators..- 8. The Hilbert Space Model for Quantum Mechanics and the EPR Dilemma.- A. A Brief History of Quantum Mechanics.- B. A Hilbert Space Model for Quantum Mechanics.- Schroedinger’s equation, probability measures, stationary states, the harmonic oscillator, the assumptions of quantum mechanics, position and momentum operators, compatibility..- C. The EPR Experiment and the Challenge of the Realists.- Electron spin, spin states, singlet state, EPR apparatus, the EPR dilemma..- Index of Definitions.
Book by Cohen David W
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
EUR 20,53 per la spedizione da U.S.A. a Italia
Destinazione, tempi e costiEUR 25,66 per la spedizione da U.S.A. a Italia
Destinazione, tempi e costiDa: Zubal-Books, Since 1961, Cleveland, OH, U.S.A.
Condizione: Very Good. *Price HAS BEEN REDUCED by 10% until Monday, July 14 (weekend SALE ITEM)* First edition, first printing, 149 pp., Hardcover, very good. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country. Codice articolo ZB1321345
Quantità: 1 disponibili
Da: Better World Books, Mishawaka, IN, U.S.A.
Condizione: Good. Used book that is in clean, average condition without any missing pages. Codice articolo 15189334-6
Quantità: 1 disponibili
Da: Better World Books, Mishawaka, IN, U.S.A.
Condizione: Good. Former library book; may include library markings. Used book that is in clean, average condition without any missing pages. Codice articolo GRP77854853
Quantità: 1 disponibili
Da: HPB-Red, Dallas, TX, U.S.A.
Hardcover. Condizione: Good. Connecting readers with great books since 1972! Used textbooks may not include companion materials such as access codes, etc. May have some wear or writing/highlighting. We ship orders daily and Customer Service is our top priority! Codice articolo S_425770397
Quantità: 1 disponibili
Da: Toscana Books, AUSTIN, TX, U.S.A.
Hardcover. Condizione: new. Excellent Condition.Excels in customer satisfaction, prompt replies, and quality checks. Codice articolo Scanned0387968709
Quantità: 1 disponibili