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94-117_PC300690.jpg
Course description

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Information sheet

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Particle in harmonic oscillator

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Particle in harmonic oscillator (2)

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Particle in harmonic oscillator (3)

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Particle in harmonic oscillator (4)

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Particle in harmonic oscillator (5)

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Feb 2: first class

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Gaussian integration

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The Fourier transform

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Feb 4 evaluation

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Feb 4: Path integrals for the harmonic oscillator

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Another evaluation

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HW1: Fourier analysis

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Feb 7: Fourier analysis

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Feb 9: To Schroedinger's equation

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22b of Apr 27, 1992; Least action, a particle in E&M fields

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22b of Apr 29, 1992: Maxwell's equations

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Feb 11: Differential forms

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HW2: Maxwell, Lorentz transformations, free Schroedinger

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115 of Nov 27, 1991: Euler-Lagrange

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Feb 16: Maxwell

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115 of Dec 2, 1991: Power lines

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115 of Dec 4, 1991: The brachistochrone

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The brachistochrone

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Feb 18

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Evaluation

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115 of Dec 6, 1991: The isoperimetric inequality

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Feb 23: Lagrange multipliers

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Euler-Lagrange following Itzykson-Zuber

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115 of Dec 9, 1991: The Hamiltonian formulation

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Feb 24: Planning

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115 of Dec 11, 1991: Poisson brackets, Noether's theorem

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Feb 28: The Hamiltonian formulation, quantization

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March 2: Symplectic geometry

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March 4: Symplectic geometry

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March 7

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HW2 Solution

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HW2 Solution (2)

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115 of Dec 16, 1991: Noether's theorem

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Noether's theorem

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March 9: Poisoon brackets, Noether

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March 11: Noether

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Hamilton-Jacobi

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Hamilton-Jacobi (2)

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March 14 HW: Hamilton-Jacobi

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March 14: Hamilton-Jacobi

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March 14: Hamilton-Jacobi (2)

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March 16: Legendre's transform

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March 18: Second variations

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Suggested topics for projects

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March 21 HW

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March 21: Second variations

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March 23: Second variations

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First page of Mermin's paper

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Apr 4: Non-Commutative Probability

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Apr 4: Non-Commutative Probability (2)

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First page of my NCP paper

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The Heisenberg inequality (a page from my paper Two Examples in Non-Commutative Probability)

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Apr 6: Non-Commutative Probability

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April 8: Non-Commutative Probability

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Apr 11 HW: Non-Commutative Probability

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Apr 11: Non-Commutative Probability

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Planning

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The Stone - von-Neuman Uniqueness Theorem

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The Stone - von-Neuman Uniqueness Theorem (2)

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The Stone - von-Neuman Uniqueness Theorem (3)

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The Stone - von-Neuman Uniqueness Theorem (4)

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The Stone - von-Neuman Uniqueness Theorem (5)

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Apr 13: The Heisenberg inequality, SvN uniqueness

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Apr 18: SvN uniqueness

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Apr 20: SvN uniqueness, dynamics

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Apr 20: creation and annihilation

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Hermite

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Hermite (2)

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Apr 22: The harmonic oscillator

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Creation and annihilation

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Apr 27: Rotations and spin

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??

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Apr 29: Rotations and spin

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Linking numbers

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May 6: Perturbation theory

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