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 - Stern-Gerlach 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, Clebsch-Gordan 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, Walsh-Hadamard 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, Bohr-Sommerfeld 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.
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