**GRADUATE PROGRAM IN FACULTY OF PHYSICS**

In **M.Sc****. program**, every student will take 30 credits as follows:

a) 13 credits as compulsory courses (Electrodynamics, Advanced Quantum Mechanics I & II, Advanced Statistical Mechanics I)

b) 9 credits as specialized fields courses (Advanced Solid state Physics I & II , Special topics in condensed matter physics, Advanced Nuclear Physics I & II ,Special topics in nuclear physics, Advanced Particle Physics I & II and Special topics in particle physics)

c) Physics Seminar (2 Credits)

d) M.Sc. Thesis (6 Credits)

The **Ph.D**. Program has already started in academic year 1998. In that, every Ph.D. student will take 15 credits as, Advanced Solid State Physics , Many Body Theory, Advanced Statistical Mechanics, Critical Phenomenea, Advanced Condensed Matter Physics, Density functional theory , Magnetic properties of materials ,Advanced Nuclear Physics,Quantum Field Theory1 and 2, Advanced Elementary Particle Physics , ... , 1 credit as Ph.D Seminar and 20 credits as Ph.D Thesis.

**GRADUATE COURSES**

**Curriculum for the Degree of Master of Science M.Sc in Physics,**

**Major ****Solid State Physics**

**COURSE CODE COURSE TITLE CREDITS **

20-12-513 Advanced Solid State Physics I 3

20-12-514 Advanced Solid State Physics II 3

20-12-718 Magnetic Properties of Materials 3

20-10-717 Physics of Manybody Systems I 3

20-12-714 Special Topics in condensed matter 3

**Note : Only 9 credits of the above courses are necessary in M.Sc. program.**

**Curriculum for the Degree of Master of Science M.Sc. in Physics,**

**Major ****Nuclear Physics**

20-14-515 Advanced Nuclear Physics I 3

20-14-516 Advanced Nuclear Physics II 3

20-14-517 Special Topics in nuclear physics 3

**Curriculum for the Degree of Master of Science M.Sc. in Physics,**

**Major ****Particle Physics**

20-16-526 Advanced Particle Physics I 3

20-16-702 Advanced Elementary Particles II 3

20-16-723 Special Topics in particle physics 3

**GRADUATE COURSE DESCRIPTIONS**

**20-10-501 Classical Mechanics **3 Cr. A Summary of Newtonian mechanics, principle of least action, Lagrangian and Hamiltonian formulations, canonical transformations, Poison's brackets, Hamilton-Jacobi theory, introduction to classical field theory.

**20-10-506 Advanced Quantum Mechanics I **3 Cr. Fundamental concepts: Kets. bras, and operators, measurements, observables and the uncertainty relations, quantum dynamics: the Schrodinger, Heisenberg and interaction pictures, propagators and Feynman path integrals, theory of angular momentum: Addition of angular momentum, symmetry in quantum mechanics.

**20-10-507 Advanced Quantum Mechanics II **3 Cr. Approximation methods: perturbation theory, hydrogen like atoms, variational methods, energy shift and decay width, identical particles: permutation symmetry, 2 electron system, young tableaux, scattering theory: Born and Eikonal approximation, method of partial waves, identical particles and scattering and coulomb scattering.

**Prerequisite **: Advanced Quantum Mechanics I 20-10-506

**20-10-510 Electrodynamics **4 Cr. Methods of solving electrostatic boundary value problems, Green functions, physics of dielectric media, magnetostatics, dynamics of electromagnetic fields, covariant formulation of electrodynamics, interactions of relativistic charged particles and fields.

**20-10-512 Advanced Statistical Mechanics **3 Cr. The statistical basis of thermo- dynamics, elements of ensemble theory, the canonical ensemble, the grand canonical ensemble, formulation of quantum statistics, the theory of simple gases, ideal Bose systems, ideal Fermi systems.

**20-12-513 Advanced Solid State Physics I **3 Cr. Free electron models, crystal structure, electron in a weak periodic potential, methods for calculating band structures, semiclassical models of electron dynamics, fermi surfaces, pseudopotential.

**20-12-514 Advanced Solid State Physics II **3 Cr. Beyond the independent electron approx, hartree approx, hartree Fock approx, exchange correlation, surface effects, cohesive energy, Lattice dynamics, magnetism.

**Prerequisite **: Advanced Solid State I 20-12-513

**20-14-515 Advanced Nuclear Physics I **3 Cr. Nuclear reactions, reaction mechanisms, nuclear models, shell model, collective model.

**20-14-516 Advanced Nuclear Physics II **3 Cr. Nuclear orientation, nuclear forces, fundamental particles properties, classification, the weak and strong interactions, miscellaneous topics.

**Prerequisite **: Advanced Nuclear Physics I 20-14-515

**20-16-526 Advanced Particle Physics 1**

**20-16-702 Advanced Elementary Particles II**

**Prerequisite **:Advanced Particle Physics 1

**20-10-717 Subjects covered in Quantum Many-body course:**

1. Second quantization for Bosons and Fermions

- Second quantized Hamiltonian for electron gas

- Model Hamiltonians on the lattice: Hubbard, Anderson, Kondo, t-J and Heisenberg

2. Perturbation theory and its failure for jellium model

- Free Fermi gas

- Particle-hole processes and perturbation theory

3. Mean Field Theory

- Broken symmetry and order parameter

- Hartree-Fock approximation, and stoner criterion

- Spin density wave approximation

4. Equation of Motion (EOM)

- Heirarchy of EOMs

- Mean Field truncation of EOMs

- Anderson impurity model in the mean field and concept of self-energy

5. Interaction picture and Wick theorem

6. Feynman diagrams for impurity scattering

7. Feynman diagrams for electron gas

- Perturbation theory

- Random phase approximation (RPA)

- Digression on methods beyond RPA

8. Fermi liquid theory

9. Digression on other many-body techniques

- Exact diagonalization (ED)

- Quantum Monte Carlo methods (QMC)

- Dynamical Mean Field Theory (DMFT)

**Syllabus **

**20-10-724Advanced Mathematical Physics**

Textbooks:

1. Mikio Nakahara, Geometry, Topology and Physics, (IOP 2003)

2. C. Nash, S. Sen, Topology and Geometry for Physicists, (Academic Press 1987)

3. M. Fecko, Defferential Geometry and Lie Groups for Physicists, (Cambridge University Press 2006)

Contents of the Course:

1. Mathematical Preliminaries

2. Homology Groups

3. Homotopy Groups

4. Manifolds

5. De Rham Cohomology Groups

6. Riemannian Geometry

7. Complex Manifolds

**20-10-729 Critical Phenomenea**

1-Phase transitions, critical behavior

2-Scaling hypothesis and critical exponents

3-Landau-Ginzburg Hamiltonian, meanfield Theory and saddle point approximation

4-Fluctuations and correlations to saddle point approximation.

5-Renorxmalization group.

6-Series expansions

**20-12-515 Advance Physics of Solid Thin Films and Interfaces**

Prerequisite: Statistical Mechanics, Advance Solid State.

Fundamental issues related to the Deposition and Properties of Solid Thin Films and Interfaces. Including, a brief introduction to Vacuum Science and Technology, Physical and Chemical Vapor Deposition, Film Formation and Structure, Interdiffusion and Reactions in Thin Films, Mechanical Properties of Thin Films, Electrical and Magnetic properties of Thin Films, Optical Properties of Thin Films, Metallurgical and Protective Coatings, Modification of Surface and Films, Emerging Thin-Film Materials and Applications.

**20-12-713 ****Advanced**** Condensed Matter Physics **

**Linear response theory**

The general formulation of the Kubo formula is introduced and its applications for the calculations of conductivity, conductance, and dielectric function in terms of current-current correlation function and density-density correlation function is presented.

**Classical transport **

Boltzmann differential equation and its application for the DC conductivity of metals is presented. Ballistic and diffusive transport are introduced.

**Quantum transport**

Formulation of Landauer Buttiker formula is presented and the quantization of conductance is introduced.

**Disordered systems and localization**

Anderson model of disorder, Limits of weak and strong localizations, and classical and quantum percolation models are introduced.

**Microscopic BCS theory of superconductivity**

The Electron-phonon interaction is introduced using the many-body formalism and then the BCS attractive electron-electron interaction mediated by electron-phonon interaction is discussed.

**Quantum Hall effect**

The concept of Landau level quantization is presented and the current candidate mechanisms of Integer and fractional quantum Hall effect are discussed

**Fermi liquid theory**

Quasiparticle concept and the microscopic basis of the Fermi liquid theory is introduced

**20-12-715 Density functional theory**

Syllabus:

- Periodic solids and electron bands
- Integration over the Brillion zone and special points
- Adiabatic approximation
- Hellmann-Feynman theorem and virial theorem
- Statistical mechanics and the density matrix
- Independent electron approximations
- Hartree and Hartree-Fock approximation
- Uniform electron gas and simple metals
- Thomas-Fermi-Dirac approximation
- Density functional theory (Hohenberg-Kohn theorems)
- Spin density functional theory
- Finite temperature density functional theory
- Pseudopotentials
- The Kohn-Sham ansatz
- Exchange-correlation hole
- Functionals for exchange and correlation
- Quantum molecular dynamics
- Wannier functions

**20-12-718 Magnetic properties of materials**

1-Magnetostatics

2-Classical and Quantum phenomenology of magnetism

3-Quantum mechanics, magnetism and exchange in atoms and oxides

4-Quantum mechanics, magnetism and bonding in metals

5-Magnetic anisotropy

6-Magnetic domain walls and domains

7-Magnetism in nanostructures

**Reference:**

- Modern Magnetic Materials: Principals and Applications Robert C. O'Handley (2000), John Wiley & Sons
- . Simple Models of Magnetism. Ralph Skomski, (2006), Oxford graduate Texts.

**20-16-526 Advanced Particle Physics 1 course syllabus**:

·Elementary Particle Physics

The classification of elementary particles as hadrons, leptons, and gauge bosons is introduced. Quark model and its applications are presented.

·Relativistic Quantum Mechanics and Introduction to Quantum Field Theory

Relativistic quantum mechanics and concepts of quantum field theory are introduced. The Klein-Gordon equation and anti-particles are discussed.

·Dirac fermions

Dirac equation is presented. Concepts of helicity, chirality are introduced. Lorentz transformations and bilinear covariants are discussed. Charge conjugation, parity, and time reversal transformations are studied.

·Introduction to Scattering

Perturbation theory, Mandelstam variables, invariant amplitudes, differential cross section, decay rates and the crossing symmetry are presented.

·Electrodynamics

Electrodynamics of scalar particles and Dirac fermions (QED) is introduced. Feynman diagram and Feynman rules are presented. Tree-level amplitudes and the corresponding cross sections are calculated. Ward identity is discussed in the Compton scattering.

·Loop Corrections

Loop diagrams are introduced. IR and UV divergences are discussed. Lamb shift and the electrons anomalus magnetic moment are described. Renormalization of the electric charge is presented. The concept of running coupling constant in QED and QCD and their consequences are explained.

·Weak interactions

Massive vector bosons are introduced. C and P violations are explained. Four-Fermi amplitudes are presented, and the rate of nuclear and muon beta-decay and pion decay are calculated. Neutrino-electron and Neutrino quark scattering is presented. Weak neutral currents are described. Weak mixing angles (Cabibbo-GIM mechanism) and CP violation in the neutral kaon system is introduced and the CKM approach is explained.

**References:**

1.F. Halzen, and A. Martin, “Quarks and Leptons: An Introductory Course in Modern Particle Physics”.

- D. J. Griffiths, “Introduction to elementary particles”.

**Syllabus **

**20-16-702 Advanced Elementary Particles II **

Textbooks:

1. F. Halzen, A. D. Martin, Quarks and Leptons, (John Wiley & Sons 1984)

2. T. Morii, C. S. Lim, S. N. Mukherjee, The Physics of the Standard Model and Beyond, (World Scientific, 2004)

Contents of the Course:

1. Weak Interactions

2. Symmetries and Gauge Theories

3. The Standard Model of Electroweak Interactions

4. Quantum Chromodynamics

5. Nutrino Masses and Neutrino Oscillations

6. Supersymmetry

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