Author | Cohen, David W. author |
---|---|
Title | An Introduction to Hilbert Space and Quantum Logic [electronic resource] / by David W. Cohen |
Imprint | New York, NY : Springer New York, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-8841-8 |
Descript | XII, 149p. 38 illus. online resource |
1. Experiments, Measure, and Integration -- A. Measures -- B. Integration -- 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 -- B. Logics and State Functions -- 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 -- B. Projection Operators and the Projection Logic -- 6. State Space and Gleasonโs Theorem -- A. The Geometry of State Space -- B. Gleasonโs Theorem -- 7. Spectrality -- A. Finite Dimensional Spaces, the Spectral Resolution Theorem -- B. Infinite Dimensional Spaces, the Spectral Theorem -- 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 -- C. The EPR Experiment and the Challenge of the Realists -- Index of Definitions