**Lecture 1:**January 25, 2021. Review of spin operators, Pauli matrices, and Pauli matrix identities. Video of lecture 1 (40 mins).**Reading:**Review your old notes and texts on spin and Pauli matrices.**Lecture 2:**January 27, 2021. 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).**Lecture 3:**January 29, 2021. 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:**February 1, 2021. Coherent states. Video of lecture 4 (31 mins).**Lecture 5:**February 3, 2021. Squeezed states. Video of lecture 5 (32 mins).**Lecture 6:**February 5, 2021. Schroedinger factorization method. Video of Lecture 6 (36 min).**Lecture 7:**February 8, 2021. Rotations and angular momentum. Video of lecture 7 (29 min).**Lecture 8:**February 10, 2021. 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:**February 12, 2021. Center of mass, two-body problem, and translation operator in spherical harmonics. Video of lecture 9 (34 mins)**Reading:**Gottfried 6.4 and 9.1**Lecture 10:**February 15, 2021. Hydrogen via the factorization method in coordinate space. Video of lecture 10 (38 mins)-
**Lecture 11:**February 17, 2021. Cartesian factorization method for hydrogen and the momentum-space wavefunctions. Video of lecture 11 (45 mins) **Lecture 12:**February 19, 2021. Addition of angular momenta I. Video of Lecture 12 (24 min)**Reading:**Gottfried, Chapter 25.**Lecture 13:**February 22, 2021. Addition of angular momenta II. Video of Lecture 13 (26 min)-
**Lecture 14:**February 24, 2021. Nondegenerate perturbation theory. Video of Lecture 14 (24 mins) **Lecture 15:**February 26, 2021. Wigner-Brillouin perturbation theory. Video of Lecture 15 (20 mins).**Reading:**Ziman, Elements of Advanced Quantum Theory, 3.1.**Lecture 16:**March 1, 2021. Degenerate Perturbation Theory I: Formalism development. Video of Lecture 16 (26 mins)**Reading:**Gottfried, Ch. 45.2.**Lecture 17:**March 3, 2021. (Tuesday is a Monday) Degenerate Perturbation Theory II: Summary and Atomic Fine Structure. Video of Lecture 17 (26 mins)**Reading:**Gottfried, Ch. 46.**Lecture 18:**March 5, 2021. Degenerate Perturbation Theory III: Hydrogen atom in an external magnetic field. Video of Lecture 18 (26 min)**Reading:**Gottfried, Ch. 47.**Lecture 19:**March 8, 2021. Degenerate Perturbation Theory IV: The Stark effect and spin examples. Video of Lecture 19 (25 mins)**Lecture 20:**March 10, 2021. Introduction to scattering I. Video of Lecture 20 (28 mins)**Reading:**Gottfried, Ch. 14, through 14.3 only.**Lecture 21:**March 12, 2021. Introduction to scattering II. Video of Lecture 21 (19 mins)**Reading:**Gottfried, Ch. 15.**Lecture 22:**March 15, 2021. 3d scattering and the generalized optical theorem. Video of Lecture 22 (34 mins)**Lecture 23:**March 17, 2021. Partial wave scattering. Video of Lecture 23 (38 mins)**Lecture 24:**March 19, 2021. Collisional (Feshbach) resonances. Video of Lecture 24 (27 mins)**Lecture 25:**March 22, 2021. The time-dependent Schroedinger equation. Lecture 25, part I (25 min) Lecture 25, Part II (17 min)**Reading:**Ziman, Elements of Advanced Quantum Mechanics, 3.2-3.4.**Lecture 26:**March 24, 2021. The interaction representation. Lecture 26, part 1 (19 min) Lecture 26, part 2 (13 min)**Reading:**Gottfried, Ch. 54**Lecture 27:**March 26, 2021. 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).**Reading:**Gottfried, Ch. 55**Lecture 28:**April 5, 2021. An exact Time-Ordered Product. Lecture 28, part 1 (16 min) Lecture 28, part 2 (29 min)**Lecture 29:**April 7, 2021. Time-dependent perturbation theory. Lecture 29 (26 min)**Lecture 30:**April 9, 2021. Landau-Zener diabatic passage. Lecture 30 (26 min)**Lecture 31:**April 12, 2021. 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 14, 2021. Fermi's golden rule and the sudden approximation Lecture 32 (29 mins)**Reading:**Gottfried Ch. 56.3.**Lecture 33:**April 16, 2021. Photoproduction of Hydrogen Lecture 33 (30 mins)**Lecture 34:**April 19, 2021. What is a photon? Lecture 34 (52 mins)**Lecture 35:**April 21, 2021. How LIGO works. Lecture 35 (46 mins)**Lecture 36:**April 23, 2021. Fermionic creation and annihilation operators. Lecture 36 (26 mins).**Reading:**Ziman, Elements of Advanced Quantum Theory, 2.1-2.3.**Lecture 37:**April 26, 2021. Applications of creation/annihilation operators. Lecture 37 (33 mins).**Lecture 38:**April 28, 2021. The Hubbard Model Lecture 38 (35 mins)**Lecture 39:**April 30, 2021. 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).**Lecture 40:**May 3, 2021. Nagaoka Ferromagnetism. Lecture 40 (25 mins)**Reading:**H. Tasaki, Phys. Rev. B**40**9192 (1989).**Lecture 41:**May 5, 2021. Antiferromagnetism Lecture 41 (26 mins)**Reading:**E.H. Lieb, Phys. Rev. Lett.**62**, 1927 (1989); J.K. Freericks and E.H. Lieb, Phys. Rev. B**51**2812 (1995).

Last modified January 6, 2021.