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                     Harmonic oscillator & angular momentum
  Lecture 11, Tuesday, October 13 Wavefunction continuity, harmonic oscillator, coherent states.