P477 Special Topics in Quantum Mechanics

PART I: Quantum entanglement & applications:

• Density matrices
• Tensor product and entangled states coherent and squeezed states; Bell basis
• Quantum teleportation
• EPR and Bells inequalities
• Shannon entropy: Qbits, introduction to quantum computing principles; measurement and decoherence

PART II: Introduction to many particle QM:

• Creation/ Annihilation operators; Symmetization/Antisymertization; many body operators, Boson/Fermion coherent states, Grassmann algebra and Gaussian integrals using coherent states.
• Dynamical variables and dynamics of identical particles
• Applications to many body systems: Angular momentum of system of identical particles, first order perturbation in many body systems, introduction to Hartree-Fock methods.

PART III: Symmetries in QM

• Group representation, Point group symmetry, Lie Groups; Schur lemma, orthogonality theorems, irreducible representations, accidental degeneracies; Irreducible tensor operators and direct product representations, Wigner Eckart theorem
• Applications including molecular orbitals, space time symmetries of Bloch states; normal model of vibrations; characters of angular momentum states; SU(2), SU(3) representations