Syllabus for Physics 5002 (Quantum Mechanics II)

Lecture 1: January 8, 2025. Review of spin operators, Pauli matrices, and Pauli matrix identities. Video of lecture 1 (40 mins). Typeset lecture HTML lecture

Lecture 2: January 10, 2025. 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 13, 2025. 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 15, 2025. Coherent states. Video of lecture 4 (31 mins). Typeset lecture HTML lecture
Lecture 5: January 17, 2025. Squeezed states. Video of lecture 5 (32 mins). Typeset lecture HTML lecture
Martin Luther King Day: January 20, 2025. No class
Lecture 6: January 22, 2025. Schroedinger factorization method. Video of Lecture 6 (36 min). Typeset lecture HTML lecture
Lecture 7: January 24, 2025. Rotations and angular momentum. Video of lecture 7 (29 min). Typeset lecture HTML lecture
Lecture 8: January 27, 2025. 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 29, 2025. Center of mass, two-body problem, and translation operator in spherical harmonics. Video of lecture 9 (34 mins)

Lecture 10: January 31, 2025. Hydrogen via the factorization method in coordinate space. Video of lecture 10 (38 mins)
Lecture 11: February 3, 2025. Cartesian factorization method for hydrogen and the momentum-space wavefunctions. Video of lecture 11 (45 mins)
Lecture 12: February 5, 2025. Addition of angular momenta I. Video of Lecture 12 (24 min)

Lecture 13: February 7, 2025. Addition of angular momenta II. Video of Lecture 13 (26 min)
Lecture 14: February 10, 2025. Nondegenerate perturbation theory. Video of Lecture 14 (24 mins)
Lecture 15: February 12, 2025. Wigner-Brillouin perturbation theory. Video of Lecture 15 (20 mins).

Lecture 16: February 14, 2025. Degenerate Perturbation Theory I: Formalism development. Video of Lecture 16 (26 mins)

President's day: February 17, 2025. No class.
Catch-up day February 18, 2025. (Monday on a Tuesday)
Lecture 17: February 19, 2025. Degenerate Perturbation Theory II: Summary and Atomic Fine Structure. Video of Lecture 17 (26 mins)

Lecture 18: February 21, 2025. Degenerate Perturbation Theory III: Hydrogen atom in an external magnetic field. Video of Lecture 18 (26 min)

Lecture 19: February 24, 2025. Degenerate Perturbation Theory IV: The Stark effect and spin examples. Video of Lecture 19 (25 mins)
Lecture 20: February 26, 2025. Introduction to scattering I. Video of Lecture 20 (28 mins)

Lecture 21: February 28, 2025. Introduction to scattering II. Video of Lecture 21 (19 mins)

Spring Break
Lecture 22: March 10, 2025. 3d scattering and the generalized optical theorem. Video of Lecture 22 (34 mins)
Lecture 23: March 12, 2025. Partial wave scattering. Video of Lecture 23 (38 mins)
Lecture 24: March 14, 2025. Collisional (Feshbach) resonances. Video of Lecture 24 (27 mins)
Lecture 25: March 17, 2025. The time-dependent Schroedinger equation. Lecture 25, part I (25 min) Lecture 25, Part II (17 min)

Lecture 26: March 19, 2025. The interaction representation. Lecture 26, part 1 (19 min) Lecture 26, part 2 (13 min)

Lecture 27: March 21, 2025. 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 24, 2025. An exact Time-Ordered Product. Lecture 28, part 1 (16 min) Lecture 28, part 2 (29 min)
Lecture 29: March 26, 2025. Time-dependent perturbation theory. Lecture 29 (26 min)
Lecture 30: March 28, 2025. Landau-Zener diabatic passage. Lecture 30 (26 min)
Lecture 31: March 31, 2025. 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 2, 2025. Fermi's golden rule and the sudden approximation Lecture 32 (29 mins)

Lecture 33: April 4, 2025. Photoproduction of Hydrogen Lecture 33 (30 mins)
Lecture 34: April 7, 2025. What is a photon? Lecture 34 (52 mins)
Lecture 35: April 9, 2025. How LIGO works. Lecture 35 (46 mins)
Lecture 36: April 11, 2023. Fermionic creation and annihilation operators. Lecture 36 (26 mins).

Lecture 37: April 14, 2025. Applications of creation/annihilation operators. Lecture 37 (33 mins).
Lecture 38: April 16, 2025. The Hubbard Model Lecture 38 (35 mins)
Easter Break
Lecture 39: April 23, 2025. 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