QUANTUM I Lecture Coverage

Week 1

• Monday, Aug. 26, Introduction, wave/particle duality, Time-dependent Schroedinger equation.
• Wednesday, Aug. 28, Spectral decomposition, wave packets, Heisenberg uncertainty principle.
• Friday, Aug. 30, Time-independent Schroedinger equation, mathematical structure of wave-function space and discrete basis basis.

Week 2

• Monday, Sept. 2, No class (Labor Day).
• Wednesday, Sept. 4, Continuous basis, bra-ket notation, change of basis.
• Friday, Sept. 6, HW #1 due, Operators, projectors, eigenvectors and eigenvalues, spectral decomposition.

Week 3

• Monday, Sept. 9, Special guest lecturer, Prof. Bob Griffiths, Quantum properties.
• Wednesday, Sept. 11, Special guest lecturer, Prof. Bob Griffiths, HW #2 due, Born rule and measurement.
• Friday, Sept. 13, Special guest lecturer, Prof. Bob Griffiths, two-slit paradox.

Week 4

• Monday, Sept. 16, Unitary time development, unitary operators.
• Wednesday, Sept. 18, HW #3 due, Density operator.
• Friday, Sept. 20, Density operator examples, Brillouin paramagnetism, two-particle system.

Week 5

• Monday, Sept. 23, Two-particle partial trace example. QM Propagator.
• Wednesday, Sept. 25, HW #4 due. Propogator, path integral, free particle example.
• Friday, Sept. 27, Exam #1 in class.

Week 6

• Monday, Sept. 30, Harmonic oscillator. raising and lowering operators, spectrum.
• Wednesday, Oct. 2, H.O. Time evolution of mean values, molecular IR spectroscopy.
• Friday, Oct. 4, Molecular spectroscopy, Raman effect, charged oscillator in constant E field.

Week 7

• Monday, Oct. 7, Two coupled harmonic oscillators, normal modes
• Wednesday, Oct. 9, HW #5 due. Harmonic chain, classical and quantum Hamiltonians
• Friday, Oct. 11, Quantum states of Harmonic chain, phonons, inelastic neutron scattering.

Week 8

• Monday, Oct. 14, Classical/quantum continuum wave equation.
• Wednesday, Oct. 16, HW #6 due. Exam #2 in class.
• Friday, Oct. 18 no class - midsemester break.

Week 9

• Monday, Oct. 21, Harominc oscillaotr in thermal equilibrium, blackbody radiation spectrum, heat capacity of solids.
• Wednesday, Oct. 23 Angular momentum operator, spectrum
• Friday, Oct. 25 Normalized eigenstates, representations of angular momentum operators in eigenstate basis, position representation of orbital angular momentum operators.

Week 10

• Monday, Oct. 28 Angular dependence of angular momentum eigenstates, pictures of eigenstates, picture of angular momentum.
• Wednesday, Oct. 30 HW #7 due. Rotation symmetry group SO(3), angular momentum as generator of rotations.
• Friday, Nov. 1 Commutation laws for angular momentum, rotation of observables. Example, 2-D Harmonic Oscillator.

Week 11

• Monday, Nov. 4 2-D Harmonic Oscillator continued, charged particle in magnetic field.
• Wednesday, Nov. 6 HW #8 due. Central potential, coulomb interaction, radial wave functions.
• Friday, Nov. 8 Degeneracy of Coulomb interaction, SO(4) hidden symmetry.

Week 12

• Monday, Nov. 11 Hybrid orbitals. Atom in magnetic field.
• Wednesday, Nov. 13 HW #9 due. Zeeman effect, spectrum and polarization. Anomalous Zeeman effect and electron spin.
• Friday, Nov. 15 Spinors. Rotation operators for spin 12.

Week 13

• Monday, Nov. 18 Total angular momentum. Addition of two spin 1/2's.
• Wednesday, Nov. 20, HW #10 due. Addition of two arbitrary angular momenta.
• Friday, Nov. 22, Clebsch-Gordon coefficients.

Week 14

• Monday, Nov. 25, HW #11 due. Vector operators and Wigner-Eckart theorem.
• Wednesday, Nov. 27, no class (Thanksgiving break)
• Friday, Nov. 29, no class (Thanksgiving break)

Week 15

• Monday, Dec. 2, Exam #3 in class
• Wednesday, Dec. 4, no class (Prof. out of town)
• Friday, Dec. 6, HW #12 due, no class (Prof. out of town)