Syllabus
|
Course Code: PHY 401 Course Name: Advanced Quantum Mechanics |
||
| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
|---|---|---|
| 1 | Relativistic Wave Equations (14 hrs.) Klein-Gordan equation: Free particle, Charge and Current Densities, Electromagnetic potentials. Energy levels in a Coulomb Field (Hydrogen atom problem). Difficulties of Klein-Gordan equation. Dirac equation: Properties of the Dirac Matrices, Free particle solutions, Charge and Current Densities, Electromagnetic potentials. Dirac equation for a central field: Spin Angular Momentum, Approximate reduction; Spin-Orbit energy, Separation of the equation, The Hydrogen atom, Classification of energy levels, Negative energy States. |
|
| 2 | Field Quantization (12 hrs.) Lagrangian Field Theory: Canonical Quantization, Coordinates of the Field, The Classical Field Equations, Functional Derivative, Hamiltonian Formulation, Quantization of the Field, Field with more than One component, Complex Field. Non-relativistic field: Lagrangian and Hamiltonian Equations, Quantization for system of Bosons and Fermions, The N representation, Matrix representation of Creation, Annihilation and Number operators for Bosons and Fermions, Commutators and Anticommutators at Unequal Times. |
|
| 3 | Quantization of Relativistic Fields and Feynman Diagrams (12 hrs.) Relativistic Fields, Natural system of units, Quantization of Klein-Gordan field, Quantization of Dirac field, Quantization of Electromagnetic fields (in vacuum): Lagrangian and Hamiltonian Equations, Quantization Procedure, Quantized field energy. Interacting fields: Feynman Diagrams, Normal product, Dyson and Wick’s chronological products, Contraction of field operators, Wick’s theorem, Electromagnetic Coupling, The Scattering Matrix, Representation of various Scattering processes on Feynman diagrams up to second order. |
|
| 4 | Quantum theory of Radiation (12 hrs.) Classical radiation field: Transversality Condition, Fourier decomposition and radiation oscillators. Creation, Annihilation and Number operators: Quantization of radiation oscillators, Photon states. Quantized Radiation Field: Photons as quantum mechanical excitations of the radiation field, Fluctuations and the uncertainty relation, Validity of the classical description. Emission and Absorption of Photons by Atoms: Basic matrix elements for emission and absorption, Time dependent perturbation theory, Spontaneous emission in dipole approximation. |
|
