Advanced Quantum Mechanics with Applications

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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.

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What Will You Learn?

  • Learn the Advanced Quantum Mechanics with Applications

Course Content

Advanced Quantum Mechanics with Applications

  • Advanced Quantum Mechanics with Applications [Introduction Video]
    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
  • Qubits,EPR Paradox
    00:00
  • Quantum Entanglement (QE)
    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
  • Interaction of Radiation with matter, Landau levels
    00:00

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