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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.
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It's a work in progress!
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Approach
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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.
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For a better stepwise buildup of ideas see the week plan.
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7 weeks
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Week Plan
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Plan
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Order is (mostly) clockwise on main branches and
top-down thereafter. See numbering on branches.
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Some maps are large so please be patient
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Maps
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This will be the principle reference
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Lecture notes,
unpublished
, Imperial College (2002)
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[Plenio]
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Lecture notes,
unpublished
, Macquarie
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(Particularly latter chapters on formalism)
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[Cresser]
1
Quantum Computation and Quantum Information
, M.A. Nielsen and I.L.
Chuang, Cambridge University Press (2000)
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[Niesen]
2
Lectures on Quantum Theory, Mathematical and Structural
Foundations
, C.J. Isham, Imperial Colledge Press (1995)
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[Isham]
3
Quantum Physics
, M. Le Bellac, Cambridge University Press (2006)
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[Le Bellac]
4
Particularly
useful references
in preparing
these lectures
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Quantum Theory: Concepts and Methods
, Asher Peres, Kluwer Academic Publishers (2002)
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[Peres]
5
Modern Quantum Mechanics
, J.J. Sakurai, Addison-Wesley (1994)
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[Sakurai]
6
Introduction to Quantum Mechanics
, D.J. Griffiths, Prentice Hall (1995)
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[Griffith]
7
Quantum Mechanics: A modern development
, Leslie
Ballentine, World Scientific Pub. Co. (2000)
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[Ballentine]
8
Quantum Processes, Systems, and Information
, B. Schumacher
and M. Westmoreland, Cambridge University Press (2010)
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[Schumacher]
9
Refs
3
Intro
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Postulates
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Everything flows from these postulates.
We'll understand them as the course
progresses and keep refering back to them.
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Postulates
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Vector Spaces
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inner product
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norms
1
Inner-product Spaces
1
Hilbert Space
2
Spaces
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ket
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bra
1
Dual space
2
Dirac Notation
1
Density Operator
2
0
1
entanglement
2
Tensor Products
3
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Trace
4
First, how do we represent
physical states of a system?
8
Partial trace
5
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Dirac delta function
0
0
Position
1
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Momentum
2
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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
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Unitaries
2
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Projectors
3
5
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Positive Semidefinite Operators
4
Linear Operators
0
0
Operator Functions
1
Generally, how do states stransform?
3
Symmetries
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Schrodingers equation
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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
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Position and momentum in HO
1
Coherent states
2
Harmonic Oscillator
4
Example
Systems
5
Quantum
Theory