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Course11510879162 lectures

Quantum Mechanics in the Relativistic Regime

Prof. Sudhir Kumar Vempati · IISc Bangalore

Start with lecture 1 At NPTEL

Lectures

Week 1 Review of Non-relativistic QM and STR

  1. Recap of NRQM YouTube
  2. Finite Step Potential: Schrodinger equation solution YouTube
  3. Properties of wavefunction YouTube
  4. Matrix Mechanics YouTube
  5. Basics of STR YouTube
  6. Natural Units YouTube

Week 2 Foundations of RQM

  1. Relativistic effects in Quantum Mechanics YouTube
  2. Building Relativistic Wave Theories YouTube
  3. Solutions to the KG equation YouTube
  4. Introduction to Relativistic Lagrangian YouTube
  5. Scalar Quantum Electrodynamics (SQED) YouTube
  6. Non-Relativistic Limit of the KG Equation: The Schrodinger Equation YouTube

Week 3 KG And Dirac Equarions

  1. Revisiting KG Equation's Negative Energy Solutions YouTube
  2. Klein Paradox YouTube
  3. Scalar Quantum Electrodynamics (SQED) YouTube
  4. Dirac Theory YouTube
  5. Dirac Equation and its solution YouTube

Week 4 Dirac Spinors and Lie Groups

  1. Dirac Spinors YouTube
  2. Properties of Spinor YouTube
  3. Group Theory YouTube
  4. Rotation Groups and their Properties YouTube
  5. Lie Group and Lorentz Boost YouTube

Week 5 Groups, Representations, and the Lorentz Structure

  1. Group Representations - I YouTube
  2. Group Representations – II YouTube
  3. Symmetry and Isomorphism YouTube
  4. Lorentz Group - I YouTube
  5. Lorentz Group – II YouTube

Week 6 Lorentz and Poincare groups

  1. Decomposition of Lorentz Group YouTube
  2. Boost and Rotation Generators YouTube
  3. Poincare Group YouTube
  4. Representations of Poincare group YouTube
  5. Solution of Dirac equation YouTube

Week 7 Dirac Formalism: Currents, Negative Energies, and Antiparticles

  1. Properties of Dirac Spinors and Probability Currents YouTube
  2. Parity Violation and Axial Currents YouTube
  3. Dirac interpretation for Negative Energy states YouTube
  4. Dirac Hole Theory YouTube
  5. Properties and Interpretations of Anti-Particle YouTube

Week 8 Majorana Fermions: Fundamental Properties and Conditions

  1. Solutions of Massless Dirac Equation YouTube
  2. Real Solutions of Dirac Equation YouTube
  3. Properties of Majorana Fermions - I YouTube
  4. Properties of Majorana Fermions – II YouTube
  5. Examples of Majorana Fermions in different systems YouTube

Week 9 Interactions as a Perturbation to Free Theory

  1. Propagator Theory – I YouTube
  2. Propagator Theory – II YouTube
  3. Green’s Functions as Propagators YouTube
  4. Solving for Green’s function YouTube

Week 10 Scattering as a Perturbative Process (SQED)

  1. Photon Propagator YouTube
  2. KG Propagator and its Properties YouTube
  3. Scattering in SQED YouTube
  4. Pion-Pion Scattering Channels YouTube
  5. Pion-Pion Matrix Amplitude YouTube

Week 11 Scattering processes in QED

  1. Dirac Propagator and its Properties YouTube
  2. Dyson equation and series YouTube
  3. QED (Compton Scattering) YouTube
  4. Dynamical Photon field processes YouTube
  5. Employing trace theorems to calculate matrix element YouTube

Week 12 QED (loop) corrections to Non-Relativistic Quantum mechanics

  1. Tree level QED processes YouTube
  2. Pion mediated Processes YouTube
  3. Loops and Renormalization YouTube
  4. Bound states in RQM YouTube
  5. Non-relativistic reduction of Dirac equation YouTube
  6. Relativistic Corrections to H atom YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISc Bangalore
Department
Physics
Teacher
Prof. Sudhir Kumar Vempati
Level
Undergraduate
Language
English
Subjects
Physics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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