Syllabus for Physics 5002 (Quantum Mechanics II)

Lecture 1: January 7, 2026. Review of spin operators, Pauli matrices, and Pauli matrix identities. Video of lecture 1 (40 mins). Typeset lecture HTML lecture

Lecture 2: January 9, 2026. 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). Typeset lecture HTML lecture
Lecture 3: January 12, 2026. Algebraic derivation of the simple harmonic oscillator wavefunction. Video of lecture 3 (40 mins). Typeset lecture HTML lecture

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

Lecture 4: January 14, 2026. Coherent states. Video of lecture 4 (31 mins). Typeset lecture HTML lecture
Lecture 5: January 16, 2026. Squeezed states. Video of lecture 5 (32 mins). Typeset lecture HTML lecture
Martin Luther King Day: January 19, 2026. No class
Lecture 6: January 21, 2026. Schroedinger factorization method. Video of Lecture 6 (36 min). Typeset lecture HTML lecture
Lecture 7: January 23, 2026. Rotations and angular momentum. Video of lecture 7 (29 min). Typeset lecture HTML lecture
Lecture 8: January 26, 2026. Spherical harmonics, the algebraic way. Video of lecture (26 min).Typeset lecture HTML lecture

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

Lecture 9: January 28, 2026. Center of mass, two-body problem, and translation operator in spherical harmonics. Video of lecture 9 (34 mins) Typeset lecture HTML lecture

Lecture 10: January 30, 2026. Hydrogen via the factorization method in coordinate space. Video of lecture 10 (38 mins)Typeset lecture HTML lecture
Lecture 11: February 2, 2026. Cartesian factorization method for hydrogen and the momentum-space wavefunctions. Video of lecture 11 (45 mins)Typeset lecture HTML lecture
Lecture 12: February 4, 2026. Addition of angular momenta I. Video of Lecture 12 (24 min) Typeset lecture HTML lecture

Lecture 13: February 6, 2026. Addition of angular momenta II. Video of Lecture 13 (26 min)Typeset lecture HTML lecture
Lecture 14: February 9, 2026. Nondegenerate perturbation theory. Video of Lecture 14 (24 mins) Typeset lecture HTML lecture
Lecture 15: February 11, 2026. Wigner-Brillouin perturbation theory. Video of Lecture 15 (20 mins). Typeset lecture HTML lecture

Lecture 16: February 13, 2026. Degenerate Perturbation Theory I: Formalism development. Video of Lecture 16 (26 mins) Typeset lecture HTML lecture

President's day: February 16, 2026. No class.
Catch-up day February 17, 2026. (Monday on a Tuesday)
Lecture 17: February 18, 2026. Degenerate Perturbation Theory II: Summary and Atomic Fine Structure. Video of Lecture 17 (26 mins) Typeset lecture HTML lecture

Lecture 18: February 20, 2026. Degenerate Perturbation Theory III: Hydrogen atom in an external magnetic field. Video of Lecture 18 (26 min) Typeset lecture HTML lecture

Lecture 19: February 23, 2026. Degenerate Perturbation Theory IV: The Stark effect and spin examples. Video of Lecture 19 (25 mins) Typeset lecture HTML lecture
Lecture 20: February 25, 2026. Introduction to scattering I. Video of Lecture 20 (28 mins) Typeset lecture HTML lecture

Lecture 21: February 27, 2026. Introduction to scattering II. Video of Lecture 21 (19 mins) Typeset lecture HTML lecture

Spring Break
Lecture 22: March 9, 2026. 3d scattering and the generalized optical theorem. Video of Lecture 22 (34 mins) Typeset lecture HTML lecture
Lecture 23: March 11, 2026. Partial wave scattering. Video of Lecture 23 (38 mins) Typeset lecture HTML lecture
Lecture 24: March 13, 2026. Collisional (Feshbach) resonances. Video of Lecture 24 (27 mins) Typeset lecture HTML lecture
Lecture 25: March 16, 2026. The time-dependent Schroedinger equation. Lecture 25, part I (25 min) Lecture 25, Part II (17 min) Typeset lecture HTML lecture

Lecture 26: March 18, 2026. The interaction representation. Lecture 26, part 1 (19 min) Lecture 26, part 2 (13 min) Typeset lecture HTML lecture

Lecture 27: March 20, 2026. 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). Typeset lecture HTML lecture

Lecture 28: March 23, 2026. An exact Time-Ordered Product. Lecture 28, part 1 (16 min) Lecture 28, part 2 (29 min) Typeset lecture HTML lecture
Lecture 29: March 25, 2026. Time-dependent perturbation theory. Lecture 29 (26 min) Typeset lecture HTML lecture
Lecture 30: March 27, 2026. Landau-Zener diabatic passage. Lecture 30 (26 min) Typeset lecture HTML lecture
Lecture 31: March 30, 2025. Simulating quantum problems with ion traps.Lecture 31, part 1 (20 min) Lecture 31, part 2 (29 min) Typeset lecture HTML lecture

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 1, 2025. Fermi's golden rule and the sudden approximation Lecture 32 (29 mins) Typeset lecture HTML lecture

Easter Break
Lecture 33: April 8, 2026. Photoproduction of Hydrogen Lecture 33 (30 mins) Typeset lecture HTML lecture
Lecture 34: April 10, 2026. What is a photon? Lecture 34 (52 mins) Typeset lecture HTML lecture
Lecture 35: April 13, 2026. How LIGO works. Lecture 35 (46 mins) Typeset lecture HTML lecture
Lecture 36: April 15, 2026. Fermionic creation and annihilation operators. Lecture 36 (26 mins). Typeset lecture HTML lecture

Lecture 37: April 17, 2026. Applications of creation/annihilation operators. Lecture 37 (33 mins). Typeset lecture HTML lecture
Lecture 38: April 20, 2026. The Hubbard Model Lecture 38 (35 mins) Typeset lecture HTML lecture
Lecture 39: April 22, 2026. Two-site Hubbard model solution.Lecture 39 (32 mins)Typeset lecture HTML lecture

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).

Lecture 40: April 24, 2026. Nagaoka Ferromagnetism. Lecture 40 (25 mins) Typeset lecture HTML lecture

Lecture 41: April 27, 2026. Antiferromagnetism Lecture 41 (26 mins) Typeset lecture HTML lecture

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