General Information

Provides an introduction to concepts and techniques of quantum mechanics, at the level of An Introduction to Quantum Mechanics by Griffiths.

Prerequisites

PHYS 3316, PHYS 3317, or PHYS 3327, or appropriate mathematics course(s), coregistration in PHYS 3318, or permission of instructor. Assumes prior experience in linear algebra, differential equations, and Fourier transforms.

Topics Covered

  • Formalism (Hilbert Spaces, Inner Products, Hermitian/Unitary/Projection Operators, Measurement, Postulates of QM, Discrete Eigenstates and Eigenvalues, Time Evolution, Basis Representations, Compatible Observables, Operators with Continuous Spectra, Uncertainty Principle, Conjugate Variables)
  • Schrodinger Equation in 3D (Spherically-symmetric Potentials, Spherical Harmonics, the Radial Equation, the Hydrogen Atom, 3D harmonic oscillator, Angular Momentum Algebra, Spin Algebra, Addition of Angular Momentum, Clebsch-Gordon madness)
  • Multiple Particles (Fermions/Bosons, Symmetric/Anti-Symmetric Wave Functions, Bloch’s Theorem, Baby Band Structure, Spin Statistics, the Helium Atom, the Periodic Table, the H2 molecule)
  • Symmetries and Conservation Laws (conserved quantities, parity, translation, rotation, selection rules, degeneracy)
  • Time-independent perturbation Theory (first & second order non-degenerate perturbation theory, first order degenerate perturbation theory, Hydrogenic fine structure)
  • Variational Principle (Helium Atom, H2 molecule ion)
  • WKB (the WKB approximation, tunneling, connection formulas)
  • Scattering (partial wave analysis, Born approximation)
  • Time-Dependent Perturbation Theory (2-level systems, transition probabilities, the Adiabatic Approximation, Absorption/Emission)

Workload

Weekly problem sets (14 total), optional discussion sections, 1 mid-term exam (roughly 90 minutes), 1 final exam (2 hr 30 min) [Spring 2023]

General Advice

The standard operating procedure for physics courses at Cornell applies fairly well to this class. Lecture and recitation attendance is a good idea unless you know you can get by without it; Griffiths is the bible of this course, and is the source you should go to for practice problems, alternative explanations, and self-study; work problem sets alone first, and then in groups, etc. Griffiths really is your friend. [Spring 2023]

Testimonials

This class basically follows Griffiths, taking as a given that you know how to solve the Schrodinger Equation in 1D for the canonical examples like the infinite square well and harmonic oscillator with your eyes closed (Chapters 1-2) and assuming some familiarity with formalism (Chapter 3). In Spring 2023, the class started fairly slow, taking four weeks or so to cover formalism, and then three more weeks to cover Chapter 4 content. After that, the pace increased significantly, moving through the remainder of Griffiths at about a chapter per week. This is okay - the later chapters are less conceptually rich, not to mention shorter. The problem sets were challenging - typically three Griffiths level problems (of the two-star variety, if you are familiar with the lingo) and then one problem that is longer and deeper that the course staff cooks up. The exams were fair, but long. You will need Calc III, Linear Algebra, and Differential Equations at the 1920/2930/2940 level for this class. For those who are expecting to continue on to graduate study of physics, I highly recommend this class, because this level of quantum mechanics is typical fodder for the Q exam at many universities. [Spring 2023]

Past Offerings

Semester Professor Median Grade Syllabus
Spring 2023 Katja Nowack A- PHYS4443_SP23.pdf