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Quantum Theory, Functional Analysis and Operator Algebras

Quantum Theory, Functional Analysis and Operator Algebras

Code	13322
Year	1
Semester	S1
ECTS Credits	10
Workload	OT(30H)/TP(30H)
Scientific area	Física e Matemática
Entry requirements	None
Learning outcomes	To address the fundamentals of C* and von Neumann algebras. To acquire advanced knowledge on the spectral decomposition of self-adjoint operators, ans applications. To understand the knowledge of the Gelfand-Naimark theorem, and its relation with spectral decomposition. To address the fundamentals of quantum information and quantum computation.
Syllabus	1. Introduction to C* algebras 2. Spectral theorem for bounded self-adjoint operators 3 . Unbounded operators: spectral theorem 4. Fundamentals of Quantum Theory 5. Quantum information and quantum computation
Main Bibliography	MS Birman, MZ Solomjak 1987 Spectral Theory of Self-Adjoint Operators in Hilbert Space, D. Reidel O Bratteli, DW Robinson 2003 Operator Algebras and Quantum Statistical Mechanics 1& 2 2ed, Springer C Cohen-Tannoudji, B Diu, F Laloë 1977 Quantum Mechanics, Wiley JB Conway 1990 A Course in Functional Analysis 2ed, Springer PAM Dirac 1958 The Principles of Quantum Mechanics 4ed, Oxford Univ.Press BC Hall 2013 Quantum Theory for Mathematicians, Springer RV Kadison, JR Ringrose 1983 Fundamentals of the Theory of Operator Algebras 1, Academic Press M Le Bellac 2006 Quantum Information and Quantum Computation, Cambridge Univ.Press ND Mermin 2007 Quantum Computer Science, Cambridge Univ.Press MA Nielsen, IL Chuang 2000 Quantum Computation and Quantum Information, Cambridge Univ.Press M Reed, B Simon 1980 Methods of Modern Mathematical Physics I, Academic Press W Rudin 1991 Functional Analysis 2ed, McGraw-Hill
Language	Portuguese. Tutorial support is available in English.