Advanced Quantum Mechanics with Applications (English)

   Friday, March 08, 2024   

Starting a new Lecture Notes Series on Advanced Quantum Mechanics with Applications

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Advanced Quantum Mechanics with Applications By Lecture Notes together!

Lecture 1: Advanced Quantum Mechanics with Applications

Lecture 2: Introduction , Postulates of Quantum Mechanics

Lecture 3: Stern Gerlach Experiment, Spin Quantization, Young's Double Slit Experiment

Lecture 4: The Mathematical Formalism of Quantum Mechanics, Uncertainty Principle

Lecture 5: The Density Matrix Formalism, Expectation values of Operators

Lecture 6: Qunatum Harmonic Oscillator, Creation and annihilation Operators

Lecture 7: Coherent States and their Properties

Lecture 8: Applications of Coherent States, squeezed states

Lecture 9: Symmetries and Conservational Principles in Quantum Mechanics

Lecture 10: Rotation Operator and Invariance of Angular Momentum, Parity

Lecture 11: Spherically Symmetric System and Applications to quantum dots

Lecture 12: Spin Angular Momentum, Addition of Angular Momentum, Clebsch gordan coefficients

Lecture 13: Magnetic Hamiltonian, Heisenberg Model

Lecture 14: Nuclear Magnetic Resonance (NMR)

Lecture 15: Applications of NMR, time evolution of Magnetic Moments

Lecture 16: Introduction to Quantum Computing

Lecture 17: Qubits,EPR Paradox

Lecture 18: Quantum Entanglement (QE)

Lecture 19: Teleportation, Quantum Teleportation for one spin

Lecture 20: Entangled state for two spins

Lecture 21: Quantum Gates, Walsh Hadamard Transportation, No cloning theorem

Lecture 22: Perturbation Theory

Lecture 23: Stark Effect: First order in ground state

Lecture 24: Stark Effect: Second order in ground state

Lecture 25: Variational method, Variation of constants, Upper bound on ground state energy

Lecture 26: Application of Variational method,Hydrogen,Helium atom,Comparison with perturbation theory

Lecture 27: WKB Approximation, Bohr Sommerfeld quantization condition

Lecture 28: Summary of Approximation methods, Time dependent Perturbation Theory

Lecture 29: Time dependent Perturbation Theory, Fermi's Golden rule, Einstein's A and B coefficients

Lecture 30: Scattering Theory

Lecture 31: Linear Response Theory: Derivation of Kubo formula

Lecture 32: Quantum Dynamics: Two level system

Lecture 33: Examples

Lecture 34: Interaction of Radiation with matter, Landau levels