The MS Physics Program aims to provide advanced training in science and technology of various branches of Physics with an aim to train students with latest technologies, and to conduct an independent investigation of a research problem and establish new industry-academia linkages.
PH–5001 Methods of Mathematical Physics
Fourier series: Introduction and general properties, convergence of trigonometric series, Integral transform development of the Fourier integral, Fourier transform, inversion theorems, Fourier transform of derivatives, Laplace transform, Laplace transform of derivatives, inverse Laplace transform. Differential equations: Separation of variables in three dimensions, Boundary value problems, Green’s functions, Integral transforms, generating functions and integral equations. Calculus of variations: dependent and independent variables, Euler-Lagrange equation and applications, several independent and dependent variables, Diffusion equation, Heat Equations, Wave equations, some nonlinear equations, Klein-Gordon equation, sine-Gordon equation Burgers equation, Backlund transformation, Tensor and vector fields, Differential geometric methods.
PH–5002 Quantum Mechanics
Waves and particles: Introduction to fundamental idea of Quantum mechanics. Electromagnetic waves and photons; Light quanta and the plank-Einstein relations, wave particle duality, Analysis of young double slit experiment, Quantum unification of two aspect of light, The Principle of spectral decomposition, Material particle and matter waves; The de Broglie relations, Wave functions: the Schrodinger equation, Quantum description of a particle Wave packets; Free particle, Form of the wave packet at given time, Heisenberg uncertainty relation, Time evolution of free wave packet, Particle in a time independent Scalar potential; Separation of variables. Stationary states, one dimensional square potential. Order of magnitude of the wave length associated with the material particle, Constraints imposed by the uncertainty relation, the uncertainty relation and the atomic parameters, An experiment illustrating the uncertainty relation, A simple treatment of a two dimensional wave packet, the relation between one and three dimensional problem, One dimensional Gaussian wave packet: spreading of wave packet, Stationary state of a particle in one dimensional square well, behaviour of wave packet at a potential step. The mathematical tool of quantum mechanics: The postulates of quantum mechanics: Spin1/2 particle: The one-dimensional harmonic oscillator: General properties of angular momentum in Quantum mechanics: Particle in a central potential: the hydrogen atom
Coulomb's Law , Electric Field , Gauss's Law , Differential Form of Gauss's Law , Another Equation of Electrostatics and the Scalar Potential ,Surface Distributions of Charges and Dipoles and Discontinuities in the Electric Field and Potential , Poisson and Laplace Equations, Green's Theorem, Uniqueness of the Solution with Dirichlet or Neumann Boundary Conditions Formal Solution of Electrostatic Boundary-Value Problem with Green Function, Electrostatic Potential Energy and Energy Density; Capacitance, Variational Approach to the Solution of the Laplace and Poisson Equations, Relaxation Method for Two-Dimensional Electrostatic Problems
Boundary- Value Problems in Electrostatics-I:
Method of Images, Point Charge in the Presence of a Grounded Conducting Sphere, Point Charge in the Presence of a Charged, Insulated, Conducting Sphere, Point Charge Near Conducting Sphere at Fixed Potential, Conducting Sphere in a Uniform Electric Field by Method of Images, Green Function for the Sphere; General Solution for the Potential, Conducting Sphere with Hemispheres at Different Potentials, Orthogonal Functions and Expansions, Separation of Variables; Laplace Equation in Rectangular Coordinates, A Two-Dimensional Potential Problem; Summation of Fourier Series, Fields and Charge Densities in Two-Dimensional Corners and Along Edges, Introduction to Finite Element Analysis for Electrostatics.
Boundary- Value Problems in Electrostatics-II:
Laplace Equation in Spherical Coordinates, Legendre Equation and Legendre Polynomials, Boundary-Value Problems with Azimuthal Symmetry, Behaviour of Fields in a Conical Hole or Near a Sharp Point, Associated Legendre Functions and the Spherical Harmonics, Addition Theorem for Spherical Harmonics, Laplace Equation in Cylindrical Coordinates; Bessel Functions, Boundary-Value Problems in Cylindrical Coordinates, Expansion of Green Functions in Spherical Coordinates, Solution of Potential Problems with the Spherical Green Function. Expansion, Expansion of Green Functions in Cylindrical Coordinates, Eigenfunction Expansions for Green Functions, Mixed Boundary Conditions, Conducting Plane with a Circular Hole, Multi-poles, Electrostatics of Macroscopic Media, Dielectrics: Multi-pole Expansion, Multi-pole Expansion of the Energy of a Charge Distribution in an External Field, Elementary Treatment of Electrostatics with Ponderable Media, Boundary Value Problems with Dielectrics, Molecular Polarizability and Electric Susceptibility, Models for Electric Polarizability, Electrostatic Energy in Dielectric Media. Magnetostatics, Faraday's Law, Quasi-Static Fields: Introduction and Definitions, Biot and Savart Law, Differential Equations of Magnetostatics and Ampere's Lawn Vector Potential, Vector Potential and Magnetic Induction for a Circular Current Loop, Magnetic Fields of Localized Current Distribution, Magnetic Moment, Force and Torque on and Energy of a Localized Current Distribution in an External Magnetic Induction , Macroscopic Equations, Boundary Conditions on В and H, Methods of Solving Boundary-Value Problems in Magnetostatics, Uniformly Magnetized Sphere, Magnetized Sphere in an External Field; Permanent Magnets, Magnetic Shielding, Spherical Shell of Permeable Material in a Uniform Field, Effect of a Circular Hole in a Perfectly Conducting Plane with an Asymptotically Uniform Tangential Magnetic Field on One Side, Numerical Methods for Two-Dimensional Magnetic Fields, Faraday's Law of Induction , Energy in the Magnetic Field, Energy and Self- and Mutual Inductances, Quasi-Static Magnetic Fields in Conductors; Eddy Currents; Magnetic Diffusion, Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws: Maxwell's Displacement Current; Maxwell Equations, Vector and Scalar Potentials, Gauge Transformations, Lorenz Gauge, Coulomb Gauge, Green Functions for the Wave Equation , Retarded Solutions for the Fields: Jefimenko's Generalizations of the Coulomb and Biot- Savart Laws; Heaviside-Feynman Expressions for Fields of Point Charge, Derivation of the Equations of Macroscopic Electromagnetism, Poynting's Theorem and Conservation of Energy and Momentum for a System of Charged Particles and Electromagnetic Fields, Poynting's Theorem in Linear Dissipative Media with Losses, Poynting's Theorem for Harmonic Fields; Field Definitions of Impedance and Admittance, Transformation Properties of Electromagnetic Fields and Sources Under Rotations, Spatial Reflections, and Time Reversal, On the Question of Magnetic Monopoles, Discussion of the Dirac Quantization Condition , Polarization Potentials (Hertz Vectors).
PH–5004 Classical Mechanics
Survey of the elementary principles, Variational principles and Lagranges’s equations, Oscillations, The classical mechanics of the special theory of relativity, Hamiltonian equations of motion, canonical transformations, Hamilton-Jacobi theory and Action angle variable, Classical Chaos, Canonical perturbation theory, Introduction to the Lagrangian and Hamiltonian formulations for continuous systems and fields, Classical mechanics of liquids and deformable solids; stress, deformation and strain flow.
PH–5005 Statistical Mechanics
Intensive and extensive quantities, thermodynamic variables, thermodynamic limit, thermodynamic transformations. Classical ideal gas, first law of thermodynamics, application to magnetic systems, heat and entropy, Carnot cycle. Second law of thermodynamics, absolute temperature, temperature as integrating factor, entropy of ideal gas. Conditions for equilibrium, Helmholtz free energy, Gibbs potential, Maxwell relations, chemical potential. First-order phase transition, condition for phase coexistence. The statistical approach: phase space, distribution function, microcanonical ensemble, the most probable distribution, Lagrange multipliers. Maxwell-Boltzmann distribution: pressure of an ideal gas, equipartition of energy, entropy, relation to thermodynamics, fluctuations, Boltzmann factor. Transport phenomena: collisionless and hydrodynamic regimes, Maxwell’s demon, non-viscous hydrodynamics, sound waves, diffusion, conduction, viscosity. Quantum statistics: thermal wavelength, identical particles, Fermi and Bose statistics, pressure, entropy, free energy, equation of state, Fermi gas at low temperatures, application to electrons in solids and white dwarfs. The Bose gas: photons, phonons, Debye specific heat, Bose-Einstein condensation, equation of state, liquid helium. Canonical and grand canonical ensembles, partition function, connection with thermodynamics, fluctuations. Minimization of free energy, photon fluctuations, pair creation. The order parameter, Broken symmetry, Ising spin model, Ginsburg Landau theory, mean-field theory, critical exponents, fluctuation-dissipation theorem, correlation length, universality.
PH–5006 Methods and Techniques of Experimental Physics
Basics of X-ray diffraction, X-ray spectra, Bragg’s law and importance, construction and operation of diffractometer, data analysis, Qualitative (Hannawalt method), Quantitative (matrix flushing methods). Characterization techniques, Basics of spectroscopy and importance, Lambert-Beer’s law, Construction and Operation of spectrophotometer, Radiation detection (Detectors), Data analysis. Construction and Operation of Scanning Electron Microscope, Construction and Operation of Atomic Force Microscope, Construction and Operation of Transmission Electron Microscope and sample preparation techniques. Vacuum techniques, Production of vacuum (Vacuum pumps), Measurements of vacuum (Gauges), Leak detection.
PH–5007 Magnetism and Magnetic Materials
Introductory magnetism: Review of diamagnetism and paramagnetism, Pauli paramagnetism. Wave functions of magnetic ions (3d, 4f), spin-orbit coupling, crystal field effects. Ferro and Antiferromagnetism: Basic Phenomenon, Mean Field Theory, Thermodynamics of ferromagnetic systems. Quantum mechanical treatment, Exchange interactions, Indirect exchange (super exchange). Spin excitations, spin waves, magnons, application to the temperature dependences of magnetization and specific heat. Band ferromagnetism. Criteria for band ferromagnetism, examples of metallic ferromagnets. Anti-Ferromagnetism: Basic phenomenon, Mean Field treatment. Types of Antiferromagnets, Parallel and perpendicular susceptibilities, Spin flop transition. Ferrites and Applications of ferrites. Domain Structures and related properties of ferromagnets: Magnetic Anisotropy, basic phenomenology. Uniaxial, Cubic and surface Anisotropies. Magnetization in soft and hard magnets.
PH–5008 Material Science
Bonding in Elemental Materials Covalent, Metallic and van der Waals Bonding), Bonding in Multielement Materials (Ionic, Mixed Ionic-Covalent Bonding, Hydrogen Bonding), Effects of Nature of Bonding on Materials Properties. Basic Structural and Symmetry Concepts, Concept of Diffraction in a Periodic Lattice, Structural Information from X-ray Diffraction and other Diffraction Techniques. Crystal Structures of Metals and Ceramic Materials. Point Defects (vacancies, interstitials, impurities, F-centers) and their stability Line and Extended Defects (Dislocations, Grain Boundaries, Stacking Faults, Interfacial, Surface and Volumetric Defects). Effect of Defects on the Properties of Materials.: Amorphous Materials / Glasses (Glass formation, Glass Transition and Crystallization of Glasses, Various Glass Forming Systems). Random Closed Packing in Metallic Glasses, Continuous Random Network in Covalent Glasses. Basic Concepts, Equilibrium Phase Diagrams, Phase Transformations – Basic Concepts, Kinetics, Metastable versus Stable Transformations, Microstructure Development, Precipitation and Dispersion Hardening, Multi Component and Multi Phase Systems, Alloys, Equilibrium Structures, Phase Separation.
PH–5009 Thin Film Deposition Techniques
Nanofabrication (Nanofabrication competencies, optimizing structure-property relationships, Integrating PNPA into nanofabrication). Thin film techniques (Sputter deposition, Plasma deposition, CVD, Spin coat techniques, Surface modifications and treatments). Molecular Engineering of Surfaces (Surface derivation, Chemical treatments, Electro-polishing). Overview of MEMS. Powder metallurgy and sintering (Powder metallurgy, Ceramic preparation). Nano-particle fabrication (Synthesis Techniques, Characterization and Safety issues).
PH–5010 Fundamentals of Nanoscience
Introduction: Nanoscience vs. Nanotechnology, Sense of Scale: Macro, micro, nano, Nano in Nature: Historical Perspective. Nano Optics: In Nature (butterfly wings), Thin films interference and light interaction, LED light, wavelengths, energy and bandgaps, Nano-applications. Surface Treatments: Hydrophobic vs. Hydrophilic, Lipid bi-layers, Nano-applications, Material Structure (Crystallography): Solids-Amorphous, polycrystalline, crystalline,Miller Indices. Many faces of carbon: fullerenes (graphene, Buckey-balls, CNT), amorphous and diamonds, Surface Area (SA) to Volume (V), The relationship between SA and V, SA: V ratio of nanoparticles vs micro and macro systems,The effects of this ratio to nanotechnology with Nanotechnology applications . Physical properties at the nanoscale: In nature (Abalone Shells, Lipid bi-layers, Gecko, Spider Webs), Contact forces:Density, Buoyancy and Surface Tension with Nanoapplications. Nanotechnology Devices:Lab-on-achip, Microfluidics,BioMEMS and DNA Microarrays, The Borg. Future Trends.
PH–5011 Semiconductor Physics
Introduction/Elementary Properties of Semiconductors, Crystal Structure, Atomic Bonding, Intrinsic and Extrinsic Semiconductors, Energy Bands, Density of States, Nearly Free Electron Model, Kronig-Penny Model, Energy Bands for Intrinsic and Extrinsic Semiconductors. Semiconductor Statistics: Fermi-Dirac Statistics, Carrier Concentrations in Thermal Equilibrium in Intrinsic Semiconductors and Semiconductors with Impurity Levels. Transport Phenomena: Constant Relaxation Time, Electrical conductivity, the Hall Effect, Transverse Magnetoresistance, Scattering Mechanisms The Boltzmann Equation: The Boltzmann Transport Equation, Conductivity and Magneto-conductivity in Parabolic and Ellipsoidal Bands, Thermoelectric and Thermomagnetic Effects, Quantum Transport Excess Carriers in Semiconductors: Diffusion processes, Diffusion and Drift of Carriers, The Continuity Equation, Direct and Indirect Recombination of Electrons and Holes, Steady State Carrier Injection, Optical Absorption, Interband Transitions, Photoconductivity, Luminescence. Metal Semiconductor Contacts and PN-Junction Theory: Ohmic, Blocking and Neutral Metal-Semiconductor Contacts, PN-Junction under Equilibrium Conditions, Forward and Reverse-Biased Junctions, Reverse-Bias Breakdown, Deviations from the Simple Theory.
PH–5012 Physics of Solar Cells
Review of Semiconductor properties: Introduction to Energy Sources, Crystal Structure and Orientations, Forbidden Energy Gaps, Probability of Occupation of Allowed States, Electrons and Holes, Energy Density of Allowed States, Densities of Electrons and Holes, Band Model of a Group IV Semiconductors, Group III and V Dopants, Location of Fermi Level in Doped Semiconductors, Carrier Transport through Drift and Diffusion. Interaction of Light with Semiconductors, Recombination Processes. p-n Junction Diodes and Other Devices Structures: Electrostatic of p-n Junctions, Junction Capacitance, Carrier Injection, Diffusive Flow in Quasi- Neutral Regions, Dark and Illuminated Characteristics, Homojunctions, Semiconductor Heterojunctions, Metal- Semiconductor Heterojunctions, Low-Resistance Contacts, MIS Solar Cells, Photo electrochemical Cells, Materials and Structural Characteristics affecting Cell Performance, Short-Circuit Current Limits & Losses, Open- Circuit Voltage Limits & Losses, Effect of Temperature, Fill Factor Losses, Efficiency Measurement and its Improvements. Solar cell advancements and characterization techniques.
PH–5013 Atomic Physics
One-electron atoms: Energy levels and wave functions of hydrogen atom. Fine and Hyperfine Structure. Extension to other single valence electron atoms Two-electron atoms. Helium atom. Independent particle model. Energy level structure, Configuration interaction, Doubly excited states and inner-shell excitations. Many electron atoms. Auto-ionization. Fano’s description for an isolated auto-ionizing resonance. Multichannel Quantum Defect Theory. Multi-channel Quantum Defect Theory (Cooke and Cromer approach). Interaction between two closed channels, one open and one closed channels. Photoionization cross sections. Angular Momentum. Angular Momentum Coupling Schemes (LS, LK, jK and jj), Spherical Tensor Operators. Angular Momentum Algebra (3j, 6j and 9j symbols), Wigner Eckart Theorem. Atoms in External fields: Hydrogen Atom in electric field (spherical and parabolic states, energy levels, field ionization). Nonhydrogenic atoms (Quantum defects and energy levels, avoided crossings and “classical’ ionization. Landau Zener Effect and pulsed field ionization).
PH–5014 Atomic Spectroscopy
Spectra of alkali metals, doublet fine structure, two electron atom, Zeeman and Paschen-Back effect, X-ray spectra, general factors influencing spectral line width and line intensities, Molecular symmetry, irreducible representation, Magnetic Fields (Classical Methods of Coherent Spectroscopy: RF resonance spectroscopy, level crossing spectroscopy, Anti-crossing spectroscopy, Quantum Beats and wave packets). Atoms in Intense radiation fields. Multiphoton Absorption, Above threshold Ionization, High Harmonic Generation Laser Cooling and Trapping. Doppler Cooling, Optical molasses and traps, Sub Doppler Cooling.
PH–5015 Reservoir Physics
Petro (porosity, permeability, saturation, capillary phenomena), properties of fluids (water, oil, gas) and an introduction to reservoir. It will present the interpretation of well tests, types of recovery mechanisms (multiphase flow, primary and secondary recovery) and the field development. Reservoir Characterization and Modeling. The workflow of reservoir characterization and modeling as routinely used in the oil industry. The presentation will be illustrated by practical work using actual data. Deterministic and stochastic modeling, volumetric calculation and uncertainties will be discussed at each stage, with a focus on geology, seismic and geostatistical methods. On shore and offshore hydrocarbon exploration methods. Shallow water and deep water exploration problems.
PH–5016 X-ray Crystallography
Crystal systems, Bravais lattices and Miller indices, Point Group, space groups and systematic absences, Structure Vs lattices, Optical diffraction and the Laue and Bragg experiments, The Ewald construction, Powder diffraction techniques, Reciprocal lattices and Diffraction, Mathematical definition of reciprocal lattices and geometrical relationships to direct (Bravais)-lattices, Role of reciprocal lattice in diffraction-the condition for constructive interference, Structural factors, Integrated intensities and the phase problem, Patterson technique and direct methods, Systematic absences and symmetry, Structure refinement, least squares, Debye-Waller factors, Data collection, unit cell and symmetry, Intensities, Data reduction, Structure solutions, Finishing Touches.
PH–5017 Solid State Electronic Devices
Semiconductor Materials, Bulk Crystal Growth, Epitaxial Growth Introduction to Physical Models, Experimental Observations (The Photoelectric Effect), The Bohr Model, Quantum Mechanics, Atomic Structure (The hydrogen atom)Excess Carriers in Semiconductors (Optical Absorption, Luminescence, and Diffusion of carriers) junctions: Fabrication of p-n Junctions (Diffusion, Rapid Thermal Processing, Ion Implantation, Chemical Vapor Deposition, Photolithography, Etching, Metallization), Forward and Reverse-Biased Junctions, Metal Semiconductor Junctions, Heterojunctions field effect transistors: Transistor Operation, The Junction FET, The Metal- Semiconductor FET, The Metal-Insulator-Semiconductor FET, The MOS Field-Effect Transistor bipolar junction transistors: Fundamentals of BJT Operation, Amplification with BJTs, BJT Fabrication, Switching, Frequency Limitations, Heterojunction Bipolar Transistors optoelectronic devices: Photodiodes, Light-Emitting Diodes, Lasers, Semiconductor Lasers power devices: The p-n-p-n Diode (Basic Structure, The Two-Transistor Analogy), The Semiconductor Controlled Rectifier, Insulated Gate Bipolar Transistor, integrated circuits: Types of Integrated Circuits - micro- and nanometer scale devices, Monolithic and Hybrid Circuits, Monolithic Device Elements (CMOS Process Integration, SOI), Charge Transfer Devices (The Basic CCD, Applications of CCDs), ULSI (Logic Devices, Semiconductor Memories).
PH–5018 Growth and Characterization of Solids
Imperfections in crystals impurities. Vacancies. Grain boundaries. Dislocations. Stacking faults. Frenkel and Schottky disorder. Color centers. Polymers and ceramics. Elastic and plastic deformation. Annealing effect of imperfection on the mechanical properties of materials. Modulation spectroscopy for optical properties in solids. Crystal optics. Stress induced optical anomalies. Kinetic ordering and disordering. Ferroelectric crystals. Chemical anisotropy. Ordering of solid solution. Crystal growth. , Quantum wells, Multiquantum wells structures and super lattices, Doping super lattices, Band structure engineering of semiconductor super lattices, Quantum well lasers, Use of quantum wells in enhancement of the efficiency of solar cells, MBE, its role in forming low dimensional structures, Classical Hall Effect, Quantum Hall Effect.
PH–5019 Plasma Physics
Introduction to plasma, occurrence of plasmas in nature, concept of temperature, Debye shielding, criteria for plasmas, applications of plasma. Single particle motion, motion of charged particles in uniform E and B fields, motion of charged particles in non-uniform E and B fields, motion of charged particles in time varying E and B fields, adiabatic invariants. Plasmas as fluids, relation of plasma to ordinary electromagnetic, the fluid equation of motion, equation of continuity, the complete set of fluid equations, plasma approximations. Waves in plasmas, representation of waves, group velocity, plasma oscillations, electron plasma waves, sound waves, ion waves, validity of plasma approximation, comparison of ion wave and electron wave, electrostatic electron oscillations perpendicular to B, electrostatic ion waves perpendicular to B, the lower hybrid frequency, EM waves with Bo=0, EM waves perpendicular to Bo, cutoffs and resonances, EM waves parallel to Bo, hydromagnetic waves, magneto-sonic waves, basic nuclear fusion reaction rates and power density, radiation losses from plasmas, operational conditions, Lawson criteria, magnetic confinement fusion, inertial confinement fusion.
PH–5020 Special Topics in Advanced Physics-I
PH–5021 Special Topics in Advanced Physics-II
BS/M.Sc. in Physics (minimum 16 years of education) degree or its equivalent with a minimum CGPA of 2.00/4.00 in semester system or 60% in annual system / Term system from an HEC recognized institute/university.
The applicant must pass NTU-GAT (General) test conducted by National Textile University, as per HEC guidelines and adopted by Advanced Studies and Research Board of NTU, Faisalabad with a minimum of 50% cumulative score.
The applicant must not be already registered as a student in any other academic program in Pakistan or abroad.
Admission merit list will be prepared according to the following criteria.
|BS Physics /B.Sc. + M.Sc||40 / 20%+20% weightage|
|NTU-GAT (General Test)||40% weightage|
|Certificate Verification Fee||2000||-||-||-|
|Red Crescent Donation||100||-||-||-|
|University Card Fee||300||-||-||-|
|Student Activity Fund||2000||2000||2000||2000|
* There is no Transport Fee for Hostel Resident but they will pay hostel charges