Mathematical Physics --- Quantum Logic and Quantum Probability MAP

 Instructor:  Dr. Mihály WEINER

Text: handouts and Chapter VIII and IX of T. Matolcsi: A Concept of Mathematical Physics, Models in Mechanics. Original research papers or other original research works will not be used; nevertheless, a relevant list of them is the following:
von Neumann, J.: "Mathematische Grundlagen der Quantenmechanik", Berlin: Springer-Verlag (1932).
Birkhoff, G., and von Neumann, J.: "The Logic of Quantum Mechanics", Annals of Mathematics 37 (1936), pg. 823-843.
Einstein A., Podolsky B., Rosen N.: "Can quantum-mechanical description of physical reality be considered complete?" Physical Review 41, (1935) 777.
Gleason, A., "Measures on the Closed Subspaces of a Hilbert Space", Journal of Mathematics and Mechanics 6 (1957), pg. 885-893.
Mackey, G.: "The Mathematical Foundation of Quantum Mechanics", Benjamin Inc. (1963).
Bell, John S.: "On the Einstein Podolsky Rosen paradox", Physics 1 #3 (1964), 195.
Bell, John S.: "On the Problem of Hidden Variables in Quantum Mechanics", Reviews of Modern Physics 38 (1966), pg. 447-52.

Prerequisite: basics of classical probability theory and linear algebra.

Course description:   the course is about the non-classical calculus of probability which is behind Quantum Physics. The emphasis will be on the mathematical and philosophycal aspects (but not directly on physics). Some "paradoxes" such as the "EPR" paradox will be also discussed.