PhD Qualifier

Syllabus – Sample Exam

The candidate will be tested on the following areas of basic physics at the graduate level of course work. Syllabus for each area is described below

    • Quantum Mechanics (40%) – Postulates in Abstract Linear Algebra Language – Finite Dimensional Systems – Simple Potentials and Scattering – Uncertainty Principle – Harmonic Oscillator – Angular Momentum, Spin and Their Addition – Hydrogen Atom – Identical Particles, Bose and Fermi Statistics – Time Dependent and Time Independent Perturbation Theory – Perturbation Theory for Degenerate Levels – Fine Structure of Hydrogen Spectrum – Interaction of Electromagnetic Fields with Atoms and Electrons – Scattering Theory – Born Approximation and Partial Wave Analysis – Variational Methods – Adiabatic, Sudden and WKB Approximations – Ahronov Bohm Eff ect. Recommended Text: Principles of Quantum Mechanics by R. Shankar. Chapters 1-7 and 9-19.

 

    • Electrodynamics (25%) – Electrostatics. Coulomb’s Law, Gauss’ Law, Electrostatics Fields, Energy in the Fields, Electric Potential – Boundary Value Problems, Poisson’s and Laplace’s equations in Two and Three Dimensions, Method of Images, Multipole Expansion of Electrostatic Fields – Electric Fields in Matter, Polarization, Electric Displacement Vector, Linear Dielectrics – Magnetostatics, Biot-Savart Law, Ampere’s Law, Magnetic Vector Potential – Magnetic Fields in Matter, Magnetization, Auxiliary Field H, Diamagnets, Paramagnets and Ferromagnets – Electrodynamics, Faraday’s Law, Max well’s Equations – Energy and Momentum of Electromagnetic Fields, Poynting’s Theorem, Max well’s Stress Tensor and Angular Momentum – Electromagnetic Waves in Vacuum, Linear Homogeneous Dielectrics and Conductors, Wave Equation, Plane Wave Solution, Reflection and Transmission at Interfaces, Waveguides – Scalar and Vector Potentials, Gauge invariance – Dipole radiation and Radiation from a point charge – Special Theory of Relativity, Lorentz Transformations, Relativistic Electrodynamics. Recommended Text: Introduction to Electrodynamics by Griffiths.

 

    • Statistical Mechanics (25%) -Thermodynamic Laws and Potentials – Partition Functions – Ensembles including Micro canonical, Canonical and Grand Canonical Ensembles – Ideal Gas in diff erent Ensembles – Quantum Statistical Physics and Density Matrix – Fermion Statistics, Fermi Energy, Fermi Pressure with Applications to Solids and Stars etc. – Bose Statistics and Bose Einstein Condensation. Recommended Text: Statistical Mechanics by K. Huang.

 

  • Classical Mechaics (10%) – Lagrange and Hamiltonian Formulations – Rigid Body Dynamics – Small Oscillations and Coupled Oscillators. Recommended Text: Classical Mechanics by Goldstein, Poole and Safko.

Qualifier Exams

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