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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)

Lecture 16 - Qubits, EPR Paradox


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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