Advanced Quantum Mechanics with Applications

The Course deals with the prerequisite material for studying advanced level research in various fields of Physics, Applied Physics and Electrical Engineering. The course begins with an introduction to advanced topics, such as, the Density Matrix formalism and its applications to quantum optics. Hence angular momentum is introduced to discuss nuclear magnetic resonance. Hence basics of quantum information theory is brought into consideration with a view to explain quantum information algorithms. Quantum dynamics is hence studied with a view to understand quantum optics for driven systems. A glossary of the approximate methods is described with a few examples. Finally, basics of quantum transport is presented to understand the conductance properties of semiconductors. INTENDED AUDIENCE : UG and PG students of Electrical and Electronics Engineering/Engineering Physics/Physics PREREQUISITES : Quantum Mechanics course at the undergraduate level INDUSTRY SUPPORT : R & D sectors of semiconductor, optics industries and Lab equipment manufacturing industries.

Week 1: Introduction to Quantum Physics, Postulates, Different representations Week 2: Density Matrix formalism, Harmonic Oscillator, Applications to coherent and squeezed states, Spherically symmetric systems, Quantum dots Week 3: Spin angular momentum, Nuclear magnetic resonance Week 4: Quantum information theory, Entanglement, Shanon entropy Week 5: Quantum computing algorithms, EPR and Bell’s paradox Week 6: Quantum dynamics, periodically driven systems Week 7: Approximation methods, perturbation theory, Variational and WKB approximation. Week 8: Linear response theory, Kubo formula.