About Course
Advanced Quantum Mechanics with Applications
The Quantum Mechanics 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 are brought into consideration with a view to explain quantum information algorithms. Quantum dynamics is hence studied with a view to understanding quantum optics for driven systems.
A glossary of the approximate methods is described with a few examples. Finally, the basics of quantum transport are presented to understand the conductance properties of semiconductors.
Course Content
Advanced Quantum Mechanics with Applications

Advanced Quantum Mechanics with Applications [Introduction Video]
00:00 
Teleportation, Quantum Teleportation for one spin
00:00 
Entangled state for two spins
00:00 
Quantum Gates, Walsh Hadamard Transportation, No cloning theorem
00:00 
Perturbation Theory
00:00 
Stark Effect: First order in ground state
00:00 
Stark Effect: Second order in ground state
00:00 
Variational method, Variation of constants, Upper bound on ground state energy
00:00 
Application of Variational method,Hydrogen,Helium atom,Comparison with perturbation theory
00:00 
WKB Approximation, Bohr Sommerfeld quantization condition
00:00 
Summary of Approximation methods, Time dependent Perturbation Theory
00:00 
Time dependent Perturbation Theory, Fermi’s Golden rule, Einstein’s A and B coefficients
00:00 
Scattering Theory
00:00 
Linear Response Theory: Derivation of Kubo formula
00:00 
Quantum Dynamics: Two level system
00:00 
Examples
00:00 
Quantum Entanglement (QE)
00:00 
Qubits,EPR Paradox
00:00 
Introduction , Postulates of Quantum Mechanics
00:00 
Stern Gerlach Experiment, Spin Quantization, Young’s Double Slit Experiment
00:00 
The Mathematical Formalism of Quantum Mechanics, Uncertainty Principle
00:00 
The Density Matrix Formalism, Expectation values of Operators
00:00 
Qunatum Harmonic Oscillator, Creation and annihilation Operators
00:00 
Coherent States and their Properties
00:00 
Applications of Coherent States, squeezed states
00:00 
Symmetries and Conservational Principles in Quantum Mechanics
00:00 
Rotation Operator and Invariance of Angular Momentum, Parity
00:00 
Spherically Symmetric System and Applications to quantum dots
00:00 
Spin Angular Momentum, Addition of Angular Momentum, Clebsch gordan coefficients
00:00 
Magnetic Hamiltonian, Heisenberg Model
00:00 
Nuclear Magnetic Resonance (NMR)
00:00 
Applications of NMR, time evolution of Magnetic Moments
00:00 
Introduction to Quantum Computing
00:00 
Interaction of Radiation with matter, Landau levels
00:00