Course11510879162 lectures
Quantum Mechanics in the Relativistic Regime
Prof. Sudhir Kumar Vempati · IISc Bangalore
Lectures
Week 1 Review of Non-relativistic QM and STR
- Recap of NRQM
- Finite Step Potential: Schrodinger equation solution
- Properties of wavefunction
- Matrix Mechanics
- Basics of STR
- Natural Units
Week 2 Foundations of RQM
- Relativistic effects in Quantum Mechanics
- Building Relativistic Wave Theories
- Solutions to the KG equation
- Introduction to Relativistic Lagrangian
- Scalar Quantum Electrodynamics (SQED)
- Non-Relativistic Limit of the KG Equation: The Schrodinger Equation
Week 3 KG And Dirac Equarions
- Revisiting KG Equation's Negative Energy Solutions
- Klein Paradox
- Scalar Quantum Electrodynamics (SQED)
- Dirac Theory
- Dirac Equation and its solution
Week 4 Dirac Spinors and Lie Groups
- Dirac Spinors
- Properties of Spinor
- Group Theory
- Rotation Groups and their Properties
- Lie Group and Lorentz Boost
Week 5 Groups, Representations, and the Lorentz Structure
- Group Representations - I
- Group Representations – II
- Symmetry and Isomorphism
- Lorentz Group - I
- Lorentz Group – II
Week 6 Lorentz and Poincare groups
- Decomposition of Lorentz Group
- Boost and Rotation Generators
- Poincare Group
- Representations of Poincare group
- Solution of Dirac equation
Week 7 Dirac Formalism: Currents, Negative Energies, and Antiparticles
- Properties of Dirac Spinors and Probability Currents
- Parity Violation and Axial Currents
- Dirac interpretation for Negative Energy states
- Dirac Hole Theory
- Properties and Interpretations of Anti-Particle
Week 8 Majorana Fermions: Fundamental Properties and Conditions
- Solutions of Massless Dirac Equation
- Real Solutions of Dirac Equation
- Properties of Majorana Fermions - I
- Properties of Majorana Fermions – II
- Examples of Majorana Fermions in different systems
Week 9 Interactions as a Perturbation to Free Theory
- Propagator Theory – I
- Propagator Theory – II
- Green’s Functions as Propagators
- Solving for Green’s function
Week 10 Scattering as a Perturbative Process (SQED)
- Photon Propagator
- KG Propagator and its Properties
- Scattering in SQED
- Pion-Pion Scattering Channels
- Pion-Pion Matrix Amplitude
Week 11 Scattering processes in QED
- Dirac Propagator and its Properties
- Dyson equation and series
- QED (Compton Scattering)
- Dynamical Photon field processes
- Employing trace theorems to calculate matrix element
Week 12 QED (loop) corrections to Non-Relativistic Quantum mechanics
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.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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