Physics 6572 - Fall 2011 - Syllabus

Basic Formalism

• Dirac notation, state vectors, observables
• Unitary transformations: translations, rotations, time evolution
• Generators of Legendre transformations -> Hermitian operators
• Hermitian operators -> generators of unitary transformation

Classical mechanics

• Hamilton's Principle
• Legendre Transformations
• Canonical transformations
• Hamilton Jacobi equation

Time Evolution

• Schrodinger equation
• Schrodinger and Heisenberg pictures
• Propagators and path integrals
• Green's functions
• Aharonov-Bohn effect, Gauge transformations

Angular Momentum

• Rotations, Angular momentum operators, angular momentum addition, Clebsch Gordon Coefficients
• Density operator
• Tensor operators, Wigner Eckart theorem

Symmetries and Conservation Laws

• Parity, Time reversal

Approximation Methods

• Stationary state perturbation theory
• WKB, variational method
• Time dependent perturbation theory and atomic transition rates
• Adiabatic approximation, Berry phase

Quantum Entanglement

• Bell's inequality
• Quantum computing
• No cloning
• Quantum teleportation

Scattering

• Born approximation, partial waves, phase shifts
• Photoelectric effect