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Physics 162a
Prof. Albion Lawrence
Brandeis University
Overview
Classical Mechanics
Newtonian mechanics.
Lagrangian Mechanics
Constrained Lagrangian Systems
Symmetries and conservation laws
Hamiltonian Mechanics
Introduction to quantum mechanics
Linear algebra
Vector spaces
Linear operators
Adjoints and inner products
Spectra of Hermitian and Unitary Operators
The Rules of Quantum Mechanics
The Axioms of Quantum Mechanics.
Example: spin-1/2 particles
Entangled states and density matrices
Local Realism vs. Quantum Mechanics
Wave mechanics
Particles on a line
Compatible and incompatible measurements
Designing Hamiltonians
The Schroedinger wave function and its dynamics
Dynamics I
Interlude: two interesting systems
The Aharonov-Bohm effect
Neutrino oscillations
Examples of nonrelativistic quantum particle dynamics
The free nonrelativistic particle
The 1d square well
The simple harmonic oscillator
Two-state systems as phenomenological models
One-dimensional scattering
Periodic potentials
The Feynman Path Integral
The Rotation Group in Quantum Mechanics
Transformations and symmetries
The Rotation Group
Representations of the rotation group
Orbital Angular Momentum
Addition of Angular Momentum
Tensor operators
The Hydrogen Atom
Reduction of the Two-Body Problem
Bound state spectra for the Coulomb problem
Approximation schemes for eigenvalues
Time-independent perturbation theory
The Variational Method
The WKBJ method
Time-Dependent Perturbation Theory
Identical Particles and Second Quantization
Identical Particles
Quantization of the electromagnetic field
Appendix
Bibliography
Index
