Advanced Quantum Mechanics with Applications
Advanced Quantum Mechanics with Applications. Instructor: Prof. Saurabh Basu, Department of Physics, IIT Guwahati. 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 the 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, the basics of quantum transport are presented to understand the conductance properties of semiconductors.
(from nptel.ac.in)
Introduction to Quantum Physics 
Lecture 01  Introduction, Postulates of Quantum Mechanics 
Lecture 02  SternGerlach Experiment, Spin Quantization, Young's Double Slit Experiment 
Lecture 03  The Mathematical Formalism of Quantum Mechanics, Uncertainty Principle 
Lecture 04  The Density Matrix Formalism, Expectation Values of Operators 
Density Matrix Formalism 
Lecture 05  Quantum Harmonic Oscillator, Creation and Annihilation Operators 
Lecture 06  Coherent States and their Properties 
Lecture 07  Applications of Coherent States, Squeezed States 
Lecture 08  Symmetries and Conservation Principles in Quantum Mechanics 
Rotation and Spin Angular Momentum 
Lecture 09  Rotation Operator and Invariance of Angular Momentum, Parity 
Lecture 10  Spherically Symmetric System and Applications to Quantum Dots 
Lecture 11  Spin Angular Momentum, Addition of Angular Momentum, ClebschGordan Coefficients 
Lecture 12  Magnetic Hamiltonian, Heisenberg Model 
Nuclear Magnetic Resonance (NMR) 
Lecture 13  Nuclear Magnetic Resonance (NMR) 
Lecture 14  Applications of NMR, Time Evolution of Magnetic Moments 
Lecture 15  Introduction to Quantum Computing 
Lecture 16  Qubits, EPR Paradox 
Basics of Quantum Information 
Lecture 17  Quantum Entanglement (QE) 
Lecture 18  Teleportation, Quantum Teleportation for One Spin 
Lecture 19  Entangled State for Two Spins 
Lecture 20  Quantum Gates, WalshHadamard Transportation, No Cloning Theorem 
Approximate Methods in Quantum Mechanics 
Lecture 21  Perturbation Theory 
Lecture 22  Stark Effect: First Order in Ground State 
Lecture 23  Stark Effect: Second Order in Ground State 
Lecture 24  Variational Method, Variation of Constants, Upper Bound on Ground State Energy 
Lecture 25  Application of Variational Method 
Lecture 26  WKB Approximation, BohrSommerfeld Quantization Condition 
Approximate Methods and Special Topics 
Lecture 27  Summary of Approximation Methods, Time Dependent Perturbation Theory 
Lecture 28  Time Dependent Perturbation Theory, Fermi's Golden Rule, Einstein's A and B Coefficients 
Lecture 29  Scattering Theory 
Lecture 30  Linear Response Theory: Derivation of Kubo Formula 
Lecture 31  Quantum Dynamics: Two Level System 
Lecture 32  Examples 
Lecture 33  Interaction of Radiation with Matter, Landau Levels 
References 
Advanced Quantum Mechanics with Applications
Instructor: Prof. Saurabh Basu, Department of Physics, IIT Guwahati. The Course deals with the prerequisite material for studying advanced level research in various fields of Physics, Applied Physics and Electrical Engineering.
