Classical and Quantum Mechanics I

Catalog description

The goal of this course is to learn the essentials of classical dynamics (ħ=0) using methods that segue naturally into the study of quantum mechanics (ħ=1). Roughly the first 60% of the course will be classical mechanics and the last 40% quantum mechanics. Classical topics will include Hamiltonian and Lagrangian mechanics, the variational principle, symmetries and Noether’s theorem, Legendre and canonical transforms and phase space, Poisson brackets and generating functions, Liouville’s theorem and Hamilton-Jacobi theory, action-angle variables and canonical perturbation theory, adiabatic invariance and the KAM theorem, and the basics of fluid dynamics (optional). Quantum topics will include Hilbert spaces, probability and measurement, the Hamiltonian and time evolution, symmetries and conservation laws, mixed states and entanglement, coordinate and momentum representations, bound and scattering states in 1D quantum mechanics, coherent and squeezed states, propagators and the path integral, and the WKB approximation and Bohr-Sommerfeld quantization.