This is a two-term graduate course that covers most of the essential topics of modern nonrelativistic quantum mechanics. The course is primarily intended for graduate students with background in Physics.

__Quantum Mechanics II__

1. Addition of angular momentums and direct product space. Spin orbit interaction. Model problem: N non-interacting spin-1/2 particles and the Dicke states.

2. N-particle systems. Indistinguishable particles and Pauli exclusion principle. System of spin-1/2 particles and exchange interaction.

3. Introduction to second quatization methods. Operators on Hilbert space of Dirac states. Model problem: 1D chain of strongly-interacting spin-1/2 particles.

4. Symmetries in quantum mechanics. Invariance under unitary transformations and conservation laws. Space inversion symmetry and parity. Lattice symmetry: Bloch waves and energy bands. Time reversal symmetry and its consequences.

5. Approximation methods in quantum mechanics: variational methods, time-independent perturbation theory. Time-independent perturbation theory in case of degenerate states. Selection rules for orbital angular momentum.

6. Energy spectrum of the hydrogen atom revisited: fine structure and hyperfine splitting.

7. Hydrogen atom in static electric and magnetic fields: quadratic and linear Stark effects, Zeeman splitting and Paschen-Back effect.

8. Time-dependent perturbation theory. Interaction picture and Dyson series for the time-evolution operator. Transitions under time-dependent perturbations: adiabatic and sudden perturbations.

9. Harmonic perturbation and interaction of quantum particles with electromagnetic field. The Fermi’s golden rule. Stimulated emission and absorption of electro-magnetic waves by a quantum particle. Spontaneous emission and the Einstein coefficients. Exactly solvable time-dependent problem: two-level system approximation and the Rabi oscillations.

10. Introduction to the quantum electrodynamics (QED): quantization of electro-magnetic field. Operators for electric and magnetic fields. Photons and vacuum fluctuations of electro-magnetic field.

11. Interaction of a quantum particle with electromagnetic field revisited: beyond semi-classical description. Derivation of the rate of spontaneous emission. The Lamb shift and renormalization of electron mass.

12. Some topics of modern quantum mechanics: cavity QED and the Jaynes-Cummings Hamiltonian. Qubits and quantum computing.

13. Introduction to quantum statistical physics. Density matrix formalism and statistical ensembles. System of non-interacting quantum particles: the Boltzmann, Bose-Einstein and Fermi-Dirac distributions.

14. Description of open quantum systems. Dephasing. Density matrix approach and the master equation. Model problem: the spin-boson model and optical Bloch equations.

Students who take the course are expected to be familiar with general topics in Classical Mechanics, Electrodynamics and Calculus. This course requires a pass in A216 Quantum Mechanics I.