| Date | Topics (subject to change) | Notes, etc... | Homework |
| Jan 7 | -states as vectors in Hilbert space, eigenvectors as
orthonormal bases, measurement probabilities -example of the qubit i.e. 2 state system |
notes fancy typed notes | optional complex numbers practice: read/do question 2 in this old PHYS200 tutorial Check your solutions here |
| Jan 9 | -physical impliations of quantum superposition for experiments -examples of quantum systems with Hilbert spaces of various dimensions | notes fancy typed notes | reading for next class homework 1 for Tuesday homework 1 solutions (Webwork link is above) |
| Jan 14 | -linear operators -matrix representation of an observable -eigenvalues and eigenvectors for an operator -Hermitian operators associated with observables | notes worksheet worksheet solutions fancy typed notes | reading for lecture 4 |
| Jan 16 | -Hermitian operators associated with observables -Expectation values and uncertainty -Definition of adjoint -Quantum tomography (deducing states from measurements) | notes worksheet worksheet solutions worksheet link | |
| Jan 21 | -Implications of commuting vs noncommuting operators, quantum uncertainty -Unitary operators for physical transformations (symmetries, time evolution, etc...) -Idea of infinitesimal transformations -Relation between Infinitesimal transformations and Hermitian operators -Connection between transformations and observables | notes fancy typed notes | |
| Jan 23 | -Time evolution and the Schrodinger Equation -Conserved quantities in quantum mechanics -Energy as the conserved quantity associated with time evolution | notes fancy typed notes | homework 3 for Tuesday/Thursday |
| Jan 28 | -Symmetries in quantum mechanics -Symmetries and Conservation Laws -Solving the Schrodinger equation using energy eigenstates | ||
| Jan 30 | -Solving the Schrodinger equation using energy eigenstates -Quantum systems with an infinite dimensional Hilbert space -Translations and the momentum operator | notes Schrodinger equation worksheet solutions Translations and momentum worksheet worksheet solutions | homework 4 for Tuesday/Thursday homework 4 solutions |
| Feb 4 | -Translations and the momentum operator -Heisenberg Uncertainty Principle -Deriving the 1D Schrodinger equation | notes fancy typed notes | |
| Feb 6 | -Solving problems close to other problems: intro to perturbation theory -Intro to quantum computing | QUIZ 1 solutions notes worksheet worksheet solutions (partial) | homework 5 for Tuesday/Thursday Notes on multipart quantum systems Harmonic Oscillator Notes homework 5 solutions |
| Feb 11 | -Perturbation theory in quantum mechanics -First order corrections to energy and state | notes fancy notes: see Griffiths chapter 6.1 (7.1 in new ed) | |
| Feb 13 | -Perturbation theory: second order corrections to energy -Why is the harmonic oscillator important -Perturbation theory: examples | notes worksheet worksheet solutions Harmonic oscillator cheat sheet | homework 6 for Tuesday/Thursday (after reading week) homework 6 solutions (complete) |
| Feb 25 | -Degenerate perturbation theory -Rotations and angular momentum operators | notes fancy notes: see Griffiths chapter 6.2 (7.2), Griffiths 4.2 fancy notes on rotations | homework 7 due Tuesday March 3rd homework 7 solutions Degenerate perturbation theory sample problem |
| Feb 27 | -Rotations and angular momentum operators -The hydrogen atom - review of the leading approximation -Angular momentum and the hydrogen atom | ||
| Mar 3 | -Angular momentum and the hydrogen atom -The electron spin -Spin-orbit coupling and the fine structure of the hydrogen spectrum | notes worksheet worksheet solutions | |
| Mar 5 | MIDTERM Midterm solutions | homework 8 due Tuesday/Thursday homework 8 solutions | |
| Mar 10 | -More spin-orbit coupling, addition of angular momenta, Clebsch-Gordon coefficients, relativistic corrections | notes worksheet worksheet solutions | |
| Mar 12 | -The fine structure constant, hyperfine splitting | notes worksheet worksheet solutions: see class notes | homework 9 due Tuesday/Thusday homework 9 solutions |
| VIDEOS: | |||
Mar 17 | Hyperfine splitting wrap-up: Hyperfine splitting: review and worksheet setup Hyperfine Splitting: worksheet solutions Hyperfine Splitting: recap and applications The variational method: Variational Method: the basic idea Variation method: basic example Variational method: practical summary and tips | notes worksheet worksheet solutions | |
| Mar 19 | -Variational method applied to helium. | notes worksheet worksheet solutions | homework 10 due Tuesday/Thusday homework 10 solutions |
| Mar 24 | -Variational
method example: the hydrogen molecule ion (note: you should prioritize
the videos below on time-dependent perturbation theory. This is a
beautiful example of the variational method, but there aren't any
essentially new skills here.) -Born-Oppenheimer approximation Variational method example: the hydrogen molecule ion I Variational method example: the hydrogen molecule ion II -Time-dependent perturbation theory (prioritize these) | notes worksheet worksheet solutions | |
| Mar 26 | Note: Youtube is now setting the default resolution to Standard Definition, but you can still choose HD for better quality. -Time dependent perturbation theory for sinusoidal perturbations. -Types of atomic transitions. -Hamiltonian for a charged particle in an electromagnetic fields. -Hamiltonian for effects of an electromagnetic wave on an atom/molecule | notes (for videos) worksheet worksheet solutions Notes on charged particles in electromagnetic fields (extra) | homework 11 due Tuesday/Thusday homework 11 solutions Time-dependent perturbation theory example solution |
| Mar 31 | Atomic transitions from eletromagnetic radiation I Atomic transitions from eletromagnetic radiation II | notes (for videos) worksheet worksheet solutions | |
Apr 2 | Spontaneous emission Physics at finite temperature Rate for Spontaneous Emission: Einstein's Derivation Spontaneous Emission: Example | notes (for videos) worksheet worksheet solutions | homework 12 due Tuesday Solutions: see exam solutions above |
Apr 7 | Quantum Field Theory | QFT slides | |
| BONUS material (you are not responsible for any of this, but it's a very educational way to procrastinate!) Mini-course on quantum subsystems, ensembles and quantum measurement (~1 hour total): Part 1: Multipart quantum systems (review) Part 2: Entanglement Part 3: The state of a quantum subsystem Part 4: Ensembles of quantum states Part 5: Ensembles from the density operator Part 6: Measurement and decoherence If you are interested in how we know that quantum mechanics isn't secretly some more ordinary deterministic theory: Bell's Inequalities notes |
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