Physics 621
Fall 2026

Graduate Quantum Mechanics I 

Course Materials:

• Week 0: 8/27                     Review of Basic Quantum Mechanics
  Syllabus
  
  Thursday, August 27 Overheads -- Introductory lecture
  Lecture 0, Thursday, August 27: Course structure, 2-slit interference, superposition, measurement.
  
  Quiz on Tuesday, Sept. 1 on section 1.1 "The Stern-Gerlach Experiment" (p1-10) of Sakurai & Napolitano.
  
  
  
• Week 1: 9/1-3                     Mathematical Foundations of Quantum Mechanics
  Tuesday, September 1 Overhead -- 5-state Stern-Gerlach separation
  Lecture 1, Tuesday, September 1: Vector spaces, orthornormal basis, inner product.
  Quiz on Thursday, Sept. 3 on eigenvalues & eigenvectors for 2×2 and 3×3 matrices.
  
  Lecture 2, Thursday, September 3: Discrete Fourier space, operators, Hermitian operators, expectation value.
  
  Problem Set 1, due date: Thursday, September 10 (new due date: Friday, Sept. 11 by 7 pm)
  
  
  
• Week 2: 9/8-10                     Postulates of Quantum Mechanics
  Lecture 3, Tuesday, September 8 Change of basis, unitary transformations, postulates of QM.
  
  Lecture 4, Thursday, September 10 Postulates of QM, expectation value, commutators, variance-uncertainty.
  
  Problem Set 2, due date: Tuesday, September 22 (in class)
  
  
  
• Week 3: 9/15-17                     Observables, position, and momentum
  Lecture 5, Tuesday, September 15 Uncertainty relations, position operator, Dirac delta, momentum & translation.
  
  Lecture 6, Thursday, September 17 X & P representations, momentum eigenstates, Fourier transforms.
  
  
  
• Week 4: 9/22-24                     Hamiltonian and Schrodinger's equation
  Lecture 7, Tuesday, September 22 Time evolution operator, Hamiltonian, Schrodinger's equation.
  
  Lecture 8, Thursday, September 24 Schrodinger & Heisenberg pictures, Ehrenfest th., probability current density.
  Quiz covering important formulas for X & P representations on Thursday, Sept. 24: Quiz topics
  
  
• Week 5: 9/29-10/1                     2-level systems
  Lecture 9, Tuesday, September 29 Time-dependence with 2 states, Josephson osc., neutrino osc., avoided crossings.
  
  Midterm test covering all topics from weeks 0-5 on Thursday, Oct. 1
  
  
  
• Week 6: 10/6                         Schrodinger equation in 1D
  Lecture 10, Tuesday, October 6 Landau-Zener transitions, square well potential, harmonic oscillator.
  
  Problem Set 3, due date: Thursday, October 15 (in class)
  
  
  
• Week 7: 10/13-15                     Quantum harmonic oscillator
  Lecture 11, Tuesday, October 13 Wavefunction continuity, harmonic oscillator, coherent states.
  
  Lecture 12, Tuesday, October 15 1D Nodal theorem of QM, Wronskian theorem, "no double null" theorem.
  
  
  
• Week 8: 10/20-22                     Angular momentum basics
  Lecture 13, Tuesday, October 20 Classical rotations, angular momentum in QM, generators of rotations.
  Quiz covering important formulas for the quantum harmonic oscillator on Thursday, Oct. 22
  
  Lecture 14, Thursday, October 22 Quantization of angular momentum J, total J and Jz, ladder operators.
  
  Problem Set 4, due date: Thursday, October 29 (in class)
  
  
  
• Week 9: 10/27-29                     Spin and orbital angular momentum
  Lecture 15, Tuesday, October 27 Spin-1/2, Pauli spin matrices, rotation of a spin-1/2 spinor.
  
  Lecture 16, Thursday, October 29 Orbital angular momentum, spherical coordinates, spherical harmonics.
  
  
  
• Week 10: 11/5                          Euler angles and rotations
  No class on Tuesday, November 3, due to federal midterm elections
  
  Quiz covering important formulas for angular momentum operators on Thursday, Nov. 5
  
  Lecture 17, Thursday, November 5 Spherical harmonics (orthonormality, completeness), Euler angles.