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# Advanced Quantum Mechanics with Applications

### Overview

COURSE OUTLINE: 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.

### Syllabus

Advanced Quantum Mechanics with Applications [Introduction Video].
Introduction , Postulates of Quantum Mechanics.
Stern Gerlach Experiment, Spin Quantization, Young's Double Slit Experiment.
The Mathematical Formalism of Quantum Mechanics, Uncertainty Principle.
The Density Matrix Formalism, Expectation values of Operators.
Qunatum Harmonic Oscillator, Creation and annihilation Operators.
Coherent States and their Properties.
Applications of Coherent States, squeezed states.
Symmetries and Conservational Principles in Quantum Mechanics.
Rotation Operator and Invariance of Angular Momentum, Parity.
Spherically Symmetric System and Applications to quantum dots.
Spin Angular Momentum, Addition of Angular Momentum, Clebsch gordan coefficients.
Magnetic Hamiltonian, Heisenberg Model.
Nuclear Magnetic Resonance (NMR).
Applications of NMR, time evolution of Magnetic Moments.
Introduction to Quantum Computing.
Quantum Entanglement (QE).
Teleportation, Quantum Teleportation for one spin.
Entangled state for two spins.
Quantum Gates, Walsh Hadamard Transportation, No cloning theorem.
Perturbation Theory.
Stark Effect: First order in ground state.
Stark Effect: Second order in ground state.
Variational method, Variation of constants, Upper bound on ground state energy.
Application of Variational method,Hydrogen,Helium atom,Comparison with perturbation theory.
WKB Approximation, Bohr Sommerfeld quantization condition.
Summary of Approximation methods, Time dependent Perturbation Theory.
Time dependent Perturbation Theory, Fermi's Golden rule, Einstein's A and B coefficients.
Scattering Theory.
Linear Response Theory: Derivation of Kubo formula.
Quantum Dynamics: Two level system.
Examples.
Interaction of Radiation with matter, Landau levels.

### Taught by

NPTEL IIT Guwahati

## Reviews

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