QUANTUM I Lecture Coverage

Week 1

• Monday, Aug. 31, Classical and quantum physics: Phase space and Hilbert space. Normal operators. (Griffiths ch. 3.1-3; C-T ch. II) Lecture Notes
• Wednesday, Sept. 2, Spectral decomposition. Physical variables and properties (notes; Griffiths ch. 3.4-8, ch. 4.1-3) Lecture Notes
• Friday, Sept. 4 AM, Quantum reasoning. Negation, conjunction, incompatibility. (Griffiths, ch. 4.4-6, ch. 5.1-3) Lecture Notes
• Friday, Sept. 4 PM, Born rule for probability (notes, more notes). Density operators. (Griffiths ch. 5.4-6; C-T comp. C_III,) Lecture Notes

Week 2

• Monday, Sept. 7, Labor Day, no class
• Wednesday, Sept. 9, Composite systems and tensor products I. Definitions and mathematics. (Griffiths ch. 6; C-T ch. II-F) Lecture Notes
• Friday, Sept. 11 AM, HW discussion. Composite systems and tensor products II. Examples and conceptual issues. (C-T comp. D_III) Lecture Notes
• Friday, Sept. 11 PM, EPR paradox, Bell inequality, GHZ "experiment" (article) Lecture Notes

Week 3

• Monday, Sept. 14, Unitary dynamics. Time-development operators. Connection with Schrodinger equation and Hamiltonian. (notes; C-T comp. F_III) Lecture Notes, Addendum
• Wednesday, Sept. 16, Bloch sphere and Pauli matrices. (C-T ch. IV) Lecture Notes
• Friday, Sept. 18 AM, HW discussion, Time dependence of spin 1/2 in constant magnetic field. (C-T comp. F_IV) Lecture Notes
• Friday, Sept. 13 PM, Spin 1/2 in time-varying magnetic field. Lecture Notes

Week 4

• Monday, Sept. 21, Joint and conditional probabilities. Stochastic processes. Markov Processes. Notes on stochastic processes. Lecture Notes
• Wednesday, Sept. 23, Multiple time quantum histories. Born rules for histories. Lecture Notes
• Friday, Sept. 25 AM, HW discussion, Compatible histories, chain ket, generalized Born rule. (Griffiths, ch. 10&11, notes) Lecture Notes
• Friday, Sept. 25 PM, Consistency of histories. Beam splitter. (Griffiths, ch. 12) Lecture Notes

Week 5

• Monday, Sept. 28, Measurements (beam splitter and spin 1/2) Lecture Notes
• Wednesday, Sept. 30, Successive measurements, Exam review. Lecture Notes
• Friday, Oct. 2, Take-home midterm exam

Week 6

• Monday, Oct. 5, Double slit interference Lecture Notes
• Wednesday, Oct. 7, Mach Zehnder interferometer (Griffiths, ch. 13) Lecture Notes
• Friday, Oct. 9 AM, HW discussion, Q-bits, quantum gates, quantum Fourier Transform (Griffiths' notes) Lecture Notes
• Friday, Oct. 9 PM, Shor's factorization algorithm, no-cloning theorem, teleportation (more notes) Lecture Notes

Week 7

• Monday, Oct. 12, Infinite dimensional Hilbert space (C-T, ch. II) Lecture Notes
• Wednesday, Oct. 14, Translation and momentum operators (C-T, comp. D_II) Lecture Notes
• Friday, Oct. 16, No class, Community engagement day

Week 8

• Monday, Oct. 19, Eigenstates of position and momentum (C-T, comp. E_II) Lecture Notes
• Wednesday, Oct. 21, Momentum representation of Schrodinger equation. Heisenberg inequalities. Lecture Notes
• Friday, Oct. 23, No class, Midsemester break

Week 9

• Monday, Oct. 26, Free particle motion. Wave packet spreading. (C-T, comp. E_I - J_I)) Lecture Notes
• Wednesday, Oct. 28, Step boundary condition. Incident and reflected waves. Lecture Notes
• Friday, Oct. 30 AM, Square well bound states Lecture Notes
• Friday, Oct. 30 PM, Reflection and transmission of square well (C-T, comp. M_III, N_III) Lecture Notes

Week 10

• Monday, Nov. 2, Bound states and scattering resonances Lecture Notes
• Wednesday, Nov. 4, Potential scattering. Tunneling Lecture Notes
• Friday, Nov. 6 AM, Bloch theorem for periodic potentials (C-T, comp. O_III) Lecture Notes
• Friday, Nov. 6 PM, Band structure of periodic delta function potentials Lecture Notes

Week 11

• Monday, Nov. 9, Feynman path integral. (C-T, comp. J_III) Lecture Notes
• Wednesday, Nov. 11, Take-home midterm exam - 2 hour interval of your choice
• Friday, Nov. 13 AM, Harmonic oscillator via creation and anihilation operators. (C-T, ch. V) Lecture Notes
• Friday, Nov. 13 PM, WKB approximation Lecture Notes

Week 12

• Monday, Nov. 16, Expectation values and time evolution Lecture Notes
• Wednesday, Nov. 18, Charged oscillator in field (C-T, comp. F_V). Applications of HO to molecular IR and Raman spectroscopy. Exam discussion. Lecture Notes
• Friday, Nov. 20 AM, Coupled oscillators. Linear chain. (C-T, comp. H_V, J_V) Lecture Notes
• Friday, Nov. 20 PM, Phonons (C-T, comp. K_V). Thermal equilibrium. Lecture Notes

Week 13

• Monday, Nov. 23, Continuum limit, blackbody radiation (C-T, comp. L_V) Lecture Notes
• Wednesday, Nov. 25, No class, Thanksgiving holiday
• Friday, Nov. 27, No class, Thanksgiving holiday

Week 14

• Monday, Nov. 30, HW discussion. Specific heat of solids. Lecture Notes
• Wednesday, Dec. 2, Spectrum of angular momentum operator (C-T, ch. VI) Lecture Notes
• Friday, Dec. 4 AM, CSCO. Representations of angular momentum operator. Spherical harmonics (C-T, comp. A_VI) Lecture Notes
• Friday, Dec. 4 PM, Angular momentum and rotations (C-T, comp. B_VI) Lecture Notes

Week 15

• Monday, Dec. 7, Rotation of observables. 2D Harmonic Oscillator (C-T, comp. D_VI) Lecture Notes
• Wednesday, Dec. 9, Charged particle in magnetic field (C-T, comp. E_VI) Lecture Notes
• Friday, Dec. 11 AM, Atoms part I (C-T, ch. VII) Lecture Notes
• Friday, Dec. 11 PM, Atomic orbitals (C-T, comp. E_VII) Lecture Notes

Final Exam

• Monday, Dec. 14 1-4pm (to be solved in any 3-hour period Dec. 14-16)