Quantum Theory A Nexus mindmap Quantum theory as a framework for constructing physical theories. We'll be mostly looking at the structure of quantum theory and how it all fits together rather than at the quantum physics of particular systems. 0 It's a work in progress! 1 Approach 0 The current map is structured by general topics. This is better suited for review. Some topics require knowlege of others in a different part of the map, and some topic links are repeated. 0 For a better stepwise buildup of ideas see the week plan. 1 7 weeks 0 Week Plan 2 Plan 1 Order is (mostly) clockwise on main branches and top-down thereafter. See numbering on branches. 0 Some maps are large so please be patient 1 Maps 2 This will be the principle reference 0 Lecture notes, unpublished , Imperial College (2002) 1 [Plenio] 0 Lecture notes, unpublished , Macquarie 0 (Particularly latter chapters on formalism) 1 [Cresser] 1 Quantum Computation and Quantum Information , M.A. Nielsen and I.L. Chuang, Cambridge University Press (2000) 0 [Niesen] 2 Lectures on Quantum Theory, Mathematical and Structural Foundations , C.J. Isham, Imperial Colledge Press (1995) 0 [Isham] 3 Quantum Physics , M. Le Bellac, Cambridge University Press (2006) 0 [Le Bellac] 4 Particularly useful references in preparing these lectures 10 Quantum Theory: Concepts and Methods , Asher Peres, Kluwer Academic Publishers (2002) 0 [Peres] 5 Modern Quantum Mechanics , J.J. Sakurai, Addison-Wesley (1994) 0 [Sakurai] 6 Introduction to Quantum Mechanics , D.J. Griffiths, Prentice Hall (1995) 0 [Griffith] 7 Quantum Mechanics: A modern development , Leslie Ballentine, World Scientific Pub. Co. (2000) 0 [Ballentine] 8 Quantum Processes, Systems, and Information , B. Schumacher and M. Westmoreland, Cambridge University Press (2010) 0 [Schumacher] 9 Refs 3 Intro 0 Postulates 0 Everything flows from these postulates. We'll understand them as the course progresses and keep refering back to them. 1 Postulates 1 Vector Spaces 0 inner product 0 norms 1 Inner-product Spaces 1 Hilbert Space 2 Spaces 0 ket 0 bra 1 Dual space 2 Dirac Notation 1 Density Operator 2 0 1 entanglement 2 Tensor Products 3 0 Trace 4 First, how do we represent physical states of a system? 8 Partial trace 5 0 Dirac delta function 0 0 Position 1 0 Momentum 2 0 Angular Momentum 3 Infinite spaces 6 Bell inequalities 7 Representing physical states 2 For Normal operators 0 1 Spectral Decomposition 0 0 Hermitian Operators 1 0 Unitaries 2 0 Projectors 3 5 0 Positive Semidefinite Operators 4 Linear Operators 0 0 Operator Functions 1 Generally, how do states stransform? 3 Symmetries 0 Schrodingers equation 0 von Neuman equation 1 Hamiltonian 2 Time evolution 1 Time evolution 2 2 Angular Momentum 3 Symmetry 2 Transformation of physical states 3 0 Projectors 0 Born rule 0 observables 1 expectation values 2 Projective Measurements 1 0 Trace 2 Partial trace 3 How do we get information out? 4 Measurements 4 Two dimensional systems 0 Recent Bell tests 0 Bell inequalities 1 Free particle 2 Infinite Square Well 3 Harmonic oscillator 0 Position and momentum in HO 1 Coherent states 2 Harmonic Oscillator 4 Example Systems 5 Quantum Theory