Syllabus for Physics 5002 (Quantum Mechanics II)

Lecture 1: January 10, 2023. Review of spin operators, Pauli matrices, and Pauli matrix identities. Video of lecture 1 (40 mins).

Lecture 2: January 12, 2023. The five quantum operator identities: (i) Leibnitz, (ii) Hadamard, (iii) Baker-Campbell-Hausdorff, (iv) exponential reordering (braiding) and (v) exponential disentangling. Video of lecture 2 (38 mins).
Martin Luther King Day: January 15, 2023. No class
Lecture 3: January 17, 2023. Algebraic derivation of the simple harmonic oscillator wavefunction. Video of lecture 3 (40 mins).

Reading: Read old notes on raising and lowering operators for simple harmonic oscillator.

Lecture 4: January 19, 2023. Coherent states. Video of lecture 4 (31 mins).
Lecture 5: January 22, 2023. Squeezed states. Video of lecture 5 (32 mins).
Lecture 6: January 24, 2023. Schroedinger factorization method. Video of Lecture 6 (36 min).
Lecture 7: January 26, 2023. Rotations and angular momentum. Video of lecture 7 (29 min).
Lecture 8: January 29, 2023. Spherical harmonics, the algebraic way. Video of lecture (26 min).

Reading: M. Weitzman and J. K. Freericks, Calculating Spherical harmonics Without Derivatives Condens. Matt. Phys. 21 3302 (2018).

Lecture 9: January 31, 2023. Center of mass, two-body problem, and translation operator in spherical harmonics. Video of lecture 9 (34 mins)

Lecture 10: February 2, 2023. Hydrogen via the factorization method in coordinate space. Video of lecture 10 (38 mins)
Lecture 11: February 5, 2023. Cartesian factorization method for hydrogen and the momentum-space wavefunctions. Video of lecture 11 (45 mins)
Lecture 12: February 7, 2023. Addition of angular momenta I. Video of Lecture 12 (24 min)

Lecture 13: February 9, 2023. Addition of angular momenta II. Video of Lecture 13 (26 min)
Catch-up day February 12, 2023.
Lecture 14: February 14, 2023. Nondegenerate perturbation theory. Video of Lecture 14 (24 mins)
Lecture 15: February 16, 2023. Wigner-Brillouin perturbation theory. Video of Lecture 15 (20 mins).

President's day: February 19, 2023. No class.
Lecture 16: February 20, 2023 (Monday on a Tuesday day). Degenerate Perturbation Theory I: Formalism development. Video of Lecture 16 (26 mins)

Lecture 17: February 21, 2023. Degenerate Perturbation Theory II: Summary and Atomic Fine Structure. Video of Lecture 17 (26 mins)

Lecture 18: February 23, 2023. Degenerate Perturbation Theory III: Hydrogen atom in an external magnetic field. Video of Lecture 18 (26 min)

Lecture 19: February 26, 2023. Degenerate Perturbation Theory IV: The Stark effect and spin examples. Video of Lecture 19 (25 mins)
Lecture 20: February 28, 2023. Introduction to scattering I. Video of Lecture 20 (28 mins)

Lecture 21: March 1, 2023. Introduction to scattering II. Video of Lecture 21 (19 mins)

Spring Break
Lecture 22: March 11, 2023. 3d scattering and the generalized optical theorem. Video of Lecture 22 (34 mins)
Lecture 23: March 13, 2023. Partial wave scattering. Video of Lecture 23 (38 mins)
Lecture 24: March 15, 2023. Collisional (Feshbach) resonances. Video of Lecture 24 (27 mins)
Lecture 25: March 18, 2023. The time-dependent Schroedinger equation. Lecture 25, part I (25 min) Lecture 25, Part II (17 min)

Lecture 26: March 20, 2023. The interaction representation. Lecture 26, part 1 (19 min) Lecture 26, part 2 (13 min)

Lecture 27: March 22, 2023. Cyclotron Resonance. We start with a number of short review videos to help you understand what we are describing (it is about an hour long, but well worth it). The lectures appear at the end. Pushes and pulls (1 min). Opposites attract. (2 min) Fat arrows are fields. (9 min). Twisting magnetic needles. (3 min). Pojections to calculate forces (10 min). Right is correct (3 min). Current loop moves a bar magnet (3 min). Current loop is an effective magnet (2 min). To and Fro (1 min). The complicted motion we call precession (2 min). Motion of a current loop (2 min). Current loop in a magnetic field (6 min). Nuclear magnetic resonance (10 min) Magnetic resonance imaging (7 min). Lecture 27 (24 min).

Lecture 28: March 25, 2023. An exact Time-Ordered Product. Lecture 28, part 1 (16 min) Lecture 28, part 2 (29 min)
Lecture 29: March 27 2023. Time-dependent perturbation theory. Lecture 29 (26 min)
Easter Break
Lecture 30: April 3, 2023. Landau-Zener diabatic passage. Lecture 30 (26 min)
Lecture 31: April 5, 2023. Simulating quantum problems with ion traps.Lecture 31, part 1 (20 min) Lecture 31, part 2 (29 min)

Reading: K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, Quantum simulation of frustrated Ising spins with trapped ions, Nature, 465, 590--593 (2010).

Lecture 32: April 8, 2023. Fermi's golden rule and the sudden approximation Lecture 32 (29 mins)

Lecture 33: April 10, 2023. Photoproduction of Hydrogen Lecture 33 (30 mins)
Lecture 34: April 12, 2023. What is a photon? Lecture 34 (52 mins)
Lecture 35: April 15, 2023. How LIGO works. Lecture 35 (46 mins)
Lecture 36: April 17, 2023. Fermionic creation and annihilation operators. Lecture 36 (26 mins).

Lecture 37: April 19, 2023. Applications of creation/annihilation operators. Lecture 37 (33 mins).
Lecture 38: April 22, 2023. The Hubbard Model Lecture 38 (35 mins)
Lecture 39: April 24, 2023. Two-site Hubbard model solution.Lecture 39 (32 mins)

Reading: L.M. Falicov and R.A. Harris, Two‐Electron Homopolar Molecule: A Test for Spin‐Density Waves and Charge‐Density Waves J. Chem. Phys. 51 3153 (1969).

Reading: E.H. Lieb, Phys. Rev. Lett. 62, 1927 (1989); J.K. Freericks and E.H. Lieb, Phys. Rev. B 51 2812 (1995).

Jim Freericks, Professor of Physics, freericks@physics.georgetown.edu