qau course outlines.pdf

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PH: 301 Methods of Mathematical Physics

Review of vector analysis: definitions, rotation of coordinate axes, scalar product, cross product,

addition of vectors.

Differential operators, gradient, divergence, curl, integration of vector fields, Gauss' theorem, Stokes'

theorem, Gauss' law, Poisson's equation.

Definition of delta function, representations including plane wave expansion, generalization to 3

dimensions.

Vector analysis in curvilinear coordinates, orthogonal coordinates in R3, circular and spherical

coordinates, definition of tensors, contraction, direct product, quotient rule, pseudo tensors, dual

tensors, tensor derivative operators.

Determinants, matrices, orthogonal and unitary matrices, matrix diagonalization, trace theorem,

relation between determinants and traces.

Finite and infinite sequences, limit of a sequence.

Finite and infinite series, tests of convergence, alternating series, algebra of series, series of functions,

Taylor's expansion and power series, Bernoulli numbers, Euler-Maclaurin formula, asymptotic series,

infinite products

Fourier series and analysis, use and application to physical systems. orthogonality and orthonormality,

complete sets of functions, Gibbs phenomenon, discrete and continuous Fourier transform.

Complex algebra, functions of a complex variable, Cauchy-Riemann conditions, integration of complex

functions, calculus of residues, Cauchy's theorem, Laurent expansion, dispersion relations.

Recommended Texts:

Mathematical Methods for Physicists, by Arfken & Weber, publisher: Academic Press; 6th Edition, (2005)

Mathematical Methods for Physicists, by Tai L. Chow, publisher: Cambridge University Press, (2002)

Basic Training in Mathematics: A Fitness Program for Science Students, R. Shankar, publisher: Springer

(1995)



PH-302 Basic Electromagnetism.

Vector calculus: vector fields, divergence, curl, Laplacian, Gauss and Green theorems. Force on a charge,

work, energy. Conductors and insulators. The concept of induced charge and surface charge, the force

on a conductor.

Coulomb’s law, Electric field, electric field from continuous charge distributions, Gauss’s law with

applications, electric potential of a localized charge distribution, Poisson’s and Laplace’s equation.

Solutions of Poisson’s and Laplace’s equations in Cartesian, spherical and cylindrical coordinates.

Boundary conditions and uniqueness theorem, methods of images, charge between parallel plates,

charge outside metallic sphere, induced surface charges.

Multipole expansion, potential due to electric and magnetic monopoles and dipoles, electric and

magnetic dipoles, fields at long and short distances.

Electric polarization and induced dipoles, bound charges and field inside a dielectric, electric

displacement, Gauss’s law in the presence of dielectrics, electric susceptibility, permittivity and dielectric

constant, boundary value problems in linear dielectric medium, forces and energy in dielectric systems.

Lorentz force, magnetic induction, Biot-Savart law, magnetic induction due to a long straight current

carrying wire and for a circular loop, Hall effect in semiconductors.

Vector potential, applications of Ampere’s law, multipole expansion of the vector potential.

Introduction to magnetostatics, magnetic field inside matter and the concept of auxiliary field H.Ampere’s law in magnetized materials, magnetic susceptibility and permeability. Linear and nonlinear

media with boundary conditions

Recommended texts:

Introduction to Electrodynamics, by David J. Griffiths, publisher: Prentice-Hall; 3rd Edition, (1999).

Electromagnetic Fields and Waves, by Paul Lorrain and Dale R. Corson, publisher: S. K. Jain for CBS

publishers; 2nd Edition, (2003).



PH-304 Classical Mechanics

Functions, power series representation of an arbitrary function, kinematics, div, grad, curl. Basic

theorems (Gauss, Green).

Cylindrical and polar coordinates, expressions for velocity and acceleration, coordinate transformations,

rotating reference frames.

Newton’s laws, momentum, impulse of a force, applications.

One-dimensional simple harmonic oscillator, damped SHO, forced SHO, resonance, 3-D SHO, response

to several forces applied simultaneously, linear superposition principle.

Potential energy, conservative and non-conservative forces.

Motion in electromagnetic fields, cyclotron motion, motion in crossed electric and magnetic fields.

Rotating coordinate systems, fictitious forces.

Angular momentum and central forces, planetary motion under inverse-square force, constants of

motion, Kepler’s Laws, orbital transfers and gravitational boosts, radial oscillations about a circular orbit.

Systems of particles, motion with a variable mass, rocket motion.

Collisions, center of mass frame, elastic and inelastic collisions.

Rotations, angular momentum, moment of inertia and theorems, the inertia tensor, principal axes,

diagonalization.

Principle of least action, Brachistrochrone problem.

Generalized coordinates, Lagrangian mechanics, generalized forces, Hamilton’s principle, Hamilton’s

equations.

Coupled oscillations, normal modes, CO2 oscillation modes.

Recommended texts:

Classical Dynamics of Particles and Systems, by Stephen T. Thornton and Jerry B. Marion, publisher:

Brooks Cole; 5th revised edition, (2006).

Classical Mechanics, by Herbert Goldstein, publisher: Safko and Poole, 3rd Edition (2006).

Classical Mechanics, by John R. Taylor, publisher: University Science books, (2005).

Classical Mechanics by L. Chow, publisher John Willey (1995).



PH-305 Quantum Mechanics-I

Historical motivation: wave-particle duality, photo-electric effect, instability of atoms, black body

catastrophe.

Observables and operators, postulates of mechanics, measurement problems, the state function and

expectation values, Schrödinger wave equation.

Time-independent Schrödinger equation and one-dimensional problems, stationary states,

superposition principle, free particles, infinite and finite square well, harmonic oscillator, and delta-

function potential.

Hilbert space, Dirac notation, linear transformations, discrete and continuous basis vectors, hermitian

and unitary operators.

Compatible observables, commutators, uncertainty principle, minimum uncertainty states.

Time development of state functions, symmetries and conservation laws, conservation of parity,

operators for time and space translations.

Waves incident on potential barrier, reflection and transmission coefficients, WKB method.

Quantum mechanics in three-dimensions, cartesian and spherical forms of Schrodinger equation,

separation of variables.

Rotational symmetry, angular momentum as a generator of rotations, spherical harmonics and their

properties. Completeness and orthonormality properties.

Recommended texts:

Introductory Quantum Mechanics, by Richard L. Liboff, publisher: Addison Wesley; 4th Edition, (2002).

Introduction to Quantum Mechanics, by David J. Griffiths, publisher: Pearson Prentice Hall, 2nd Edition

(2005).

Quantum Physics by Stephen Gasiorowicz, publisher: Willey International, 3rd Edition

PH-401 Quantum Mechanics-II (Pre-requisite PH-305)

Motion of a particle in a central potential. Separation of variables, effective potential, solution for the

Coulomb problem. Spectrum of the hydrogen atom.

Spin as an internal degree of freedom, intrinsic magnetic moment, intrinsic angular momentum, spin-

orbit interaction and total angular momentum.

Identical particles: Many-particle systems, system of distinguishable noninteracting particles, systems

of identical particles, symmetrization postulate, Pauli exclusion principle and the periodic table.



Time-independent perturbation theory: Nondegenerate perturbation theory, degenerate perturbation

theory.

The variational principle: Variational theorem, variational approximation method, the ground state of

helium atom.

The WKB approximation: WKB wave functions, general connection rules across a classical turning point,

tunneling.

Time-dependent perturbation theory: A perturbed two-level system, perturbation by an

electromagnetic wave, transition into a continuum of states-Fermi’s golden rule, Oscillator strengths,

selection rules.

Scattering: Classical scattering theory, quantum scattering theory, partial wave analysis, phase shifts, the

Born approximation.

The adiabatic approximation: The adiabatic theorem, Berry’s phase, the Aharonov-Bohm effect.

Recommended texts:

Introductory Quantum Mechanics, by Richard L. Liboff, publisher: Addison Wesley; 4th Edition, (2002).

Introduction to Quantum Mechanics, by David J. Griffiths, publisher: Pearson Prentice Hall, 2nd Edition

(2005).

Quantum Physics, by Stephen Gasiorowicz, publisher: John Wiley, 3rd Edition (2005).

PH-306 Electromagnetic and Relativity Theory (Pre-req. PH-302)

Electromotive force and motional emf, Faraday’s law, induced electric field, energy stored in electric and

magnetic fields.

Current conservation, modification to Ampere’s law, magnetic charge, magnetic monopoles, Maxwell’s

equations, gauge invariance.

Conservation of momentum, Poynting’s theorem, Newton’s third law in electrodynamics, Newton’s

third law in electrodynamics, Maxwell’s stress tensor, angular momentum of fields.

Magnetic and electric polarizabilities, Maxwell equations in a medium, dielectrics and magnetic

materials, boundary conditions.

Wave equation, general solution, Fourier expansion, reflection and transmission of plane waves,

electromagnetic waves in vacuum.



Propagation of electromagnetic waves in conducting media and in ionized gases, reflection and

transmission at normal and oblique incidence, absorption and dispersion of electromagnetic waves in a

conductor.

Inertial frames, postulates of special relativity, invariant interval, Lorentz transformation, time dilation

and length contraction, relativistic Doppler shift.

Relativistic energy and momentum, four-vectors, kinematics of collisions, centre-of-mass, rapidity and

pseudo rapidity.

Four vector potentials and currents, covariant form of Maxwell equations, field strength tensor and

constructed invariants, plane-wave solutions of Maxwell equations, transversality.

Recommended texts:

Introduction to Electrodynamics, by David J. Griffiths, publisher: Prentice-Hall; 3rd Edition, (1999).

Electromagnetic Fields and Waves, by Paul Lorrain and Dale R. Corson, publisher: S. K. Jain for CBS

publishers; 2nd Edition, (2003).

PH-307 Thermal Physics

First law of thermodynamics, equilibrium, functions of state, internal energy; reversible changes,

enthalpy, heat capacities, reversible adiabatic changes.

Entropy, second law of thermodynamics, Carnot cycle; determination of entropy in irreversible

processes, the approach to equilibrium.

Microstates and macrostates, counting microstates, ensembles and ensemble averaging, approach to

equilibrium.

Classical probability, Statistical probability, axioms of probability theory, probability distributions,

discrete and continuous distributions, binomial and Gaussian distributions, central limit theorem,

combinatorics.

Microcanonical systems, definition of a quantum state, entropy and equilibrium in a microcanonical

system, the second law in statistical form (S=klnW)

Canonical ensemble, partition function, entropy in canonical system, Boltzmann distribution,

thermodynamical averages, applications to single particle, factorization of partition function.

Equipartition theorem, free energy and its minimization, Gibbs and Helmholtz free energy and

applications.



Maxwell distribution of molecular speeds, classical probability of a state, Maxwell-Boltzmann probability

distribution, density of states in k-space, distribution of speeds in a classical gas.

Black body radiation, Rayleigh-Jeans theory, Planck distribution, free energy of a photon gas, Stefan-

Boltzmann formula, phonons.

Systems with variable number of particles, chemical potential, grand canonical ensemble, relation to

thermodynamic variables.

Identical particles, fermions and bosons, partition function for identical particles, semi-classical

approximations, identical particles localized on a lattice, thermodynamic properties of a Fermi gas, low

and high temperature regions, Bose condensation, applications to neutron stars.

Recommended texts:

Introductory Statistical Mechanics, by R. Bowley and M. Sanchez. Publisher: Clarenden Press, Oxford,

2nd Edition (2000).

Thermal and Statistical Physics, by H. Gould and J.Tobochnik, Publisher: Princeton University Press.

(2010)

Introductory Statistical Physics, by K. Huang, publisher: CRC, 1st Edition (2001).

Thermal Physics, by C. Kittel and H. Kroemer, second edition, W. H. Freeman (1980)

PH-402 Atomic and Molecular Physics

The hydrogen atom, the Schrödinger equation, solution of the angular equation, solution of the radial

equation, spin of the electron, spin-orbit interaction, the fine structure of hydrogen, parity, selection

rules, transitions between fine-structure levels.

Helium, the ground state of helium, excited states of helium, spin eigenstates, transitions in helium

Many electron atoms, shell structure and the periodic table, Theoretical models for multielectron atoms,

The model of Independent Electrons, The Hartee method, The Hartree-Fock Method, Configuration

Interaction

Couplings of Angular Momenta, LS coupling scheme, jj coupling scheme, hyperfine structure and isotope

shift.

Atoms in External Fields, The Stark Effect, The Zeeman Effect (normal and anomalous Zeeman effects).

The Einstein A and B coefficients, the laser, Pumping, population inversion, rate equations and lasing

conditions, optical resonators



Fundamentals of Quantum Theory of Chemical Bonding, The Hydrogen-Molecule Ion H2+, The Tunnel

Effect, The Hydrogen Molecule H2, Covalent-Ionic Resonance, Hybridization, The π Electrons of Benzene

C6H6

Recommended Texts:

Physics of Atoms and Molecules, by B.H. Bransden and Joachain, publisher: Pearson Education 2nd

Edition (2003)

Atoms, Molecules and Photons, by W. Demtroder, publisher: Springer (2005)

The Physics of Atoms and Quanta, by H. Haken and H.C. Wolf, publisher: Springer 7th Edition (2004)

Atomic Physics, by C.J. Foot, publisher: Oxford University Press 1st Edition (2005).

PH-404 Sub-Atomic Physics I

Review of accelerators, cross sections, luminosity, electrostatic generators (Van de Graaff), linearaccelerators (Linacs), beam optics, synchrotrons.

Collisons, flux, intensity, laboratory and center-of-momentum frames, colliding beams, super-

conducting linacs, beam storage and cooling.

Passage of radiation through matter, heavy charged particles, photons, electrons, detectors, scintillation

counters, simple derivation of Bethe formula, statistical aspects.

A first glance at the subatomic zoo: particles and antiparticles, gauge bosons, leptons, quarks, meson

and baryon ground states.

Rutherford and Mott scattering, form factors, the charge distribution of spherical nuclei, leptons as

point probes, nucleon elastic form factors, charge radii of pion and kaon.

Inelastic electron and muon scattering, deep inelastic electron scattering, structure function for a point

particle.

Nuclear structure: Weizacker mass formula, volume and surface energies, valley of stability, liquid drop

model, fermi gas model.

Shell model: magic numbers and closed shells, spin – orbit interaction, isobaric analog resonances,

coupling with electromagnetic field. Collective model, nuclear deformations, rotational spectra of

spinless nuclei, rotational families, one-particle motion in deformed nuclei (Nilsson model), vibrational

states in spherical nuclei, interacting boson model, highly excited states, giant resonances.

General description of fission, understanding through liquid drop and collective models, application to

power generation and radioactive dating.



Outline of Big Bang cosmology, primordial nucleosynthesis, stellar energy and nucleosynthesis, stellar

collapse and neutron stars, cosmic rays, neutrino astronomy and cosmology, leptogenesis as basis for

baryon excess.

Recommended texts:

Subatomic Physics, byErnest M. Henley and Alejandro Garcia, publisher: World Scientific Publishing

(2007).

Particles and Nuclei: an Introduction to the Physical Concepts, by Povh B, Rith K, Scholz C and Zetsche F,

publisher: Berlin Springer, 5th Edition (2006).

Nuclear and Particle Physics, by Martin B R, publisher: New York: Wiley (2006)

PH-502 Sub-atomic Physics II

Additive conservation laws, conserved quantities and symmetries, electric charge, baryon number,

lepton and lepton flavor number, strangeness and flavor, additive quantum numbers of quarks.

Electromagnetic interaction, electromagnetic scattering of leptons, vector mesons as mediators of the

photon-hadron interaction, electron – positron collisions and quarks, photon –hadron interaction, real

and spacelike photons.

Importance of P,C,CP, and T in elementary particle physics, parity operation, intrinsic parities,

conservation and breakdown of parity, charge conjugation, time reversal, two-state problem, neutral

kaons, fall of CP invariance.

Weak interactions, muon decay, weak current of leptons, chirality versus helicity, the weak coupling

constant gf, weak decays of quarks and the CKM matrix, weak currents in nuclear physics, inverse beta

decay, detection of neutrons, massive neutrinos, Majorana versus Dirac neutrinos, weak current of

hadrons at high energies,

Introduction to gauge theories, Aharonov – Bohm effect, gauge invariance for non-abelian fields, Higgs

mechanisms, spontaneous symmetry breaking, gauge bosons and weak isospin, electroweak interaction,

tests of the standard model, quantum chromodynamics, QCD at low energies.

Range and strength of the low-energy strong interaction, Pion – nucleon interaction, Yukawa theory of

nuclear forces, low-energy nucleon – nucleon force, meson theory of the nucleon – nucleon force,

strong processes at high energies.

Overview: grand unified theories, supersymmetry, string theories

Recommended texts:

Subatomic Physics, Ernest M. Henley and Alejandro Garcia, World Scientific Publishing, 2007.



Particles and Nuclei: an Introduction to the Physical Concepts, by Povh B, Rith K, Scholz C and Zetsche F,

publisher: Berlin Springer, 5th Edition (2006).

Nuclear and Particle Physics, Martin B R, publisher: New York: Wiley (2006)

An Introduction to the Standard Model of Particle Physics (Kindle Edition) by W. N. Cottingham (Author),

D. A. Greenwood, 2007.

PH-503 Lasers and Quantum Optics

Review of quantum mechanics, Dirac’s notation, Pauli spin matrices, electromagnetic waves and

photons, wavelength and frequencies of electromagnetic radiation.

Spontaneous and stimulated emission, absorption. Maser principle, cavity, gain medium, population

inversion, Boltzmann statistics, threshold condition.

Three-level laser, properties of a laser beams, black-body radiation theory. Modes of a rectangular

cavity, Raleigh-Jeans and Planck radiation formula.

Semi-classical treatment of the interaction of radiation and matter. Radiative transition rates,

Interaction Hamiltonian, dipole approximation, rotating-wave approximation, electric dipole moment,

allowed and forbidden transitions, ratio of the electric-dipole transition probability to the magnetic

dipole transition probability, transition cross-section, absorption and gain coefficients.

Line-broadening mechanisms. Homogeneous broadening, collision broadening and natural broadening.

Wiener-Kinchine and Parseval’s theorem. Inhomogeneous and Doppler broadening.

Rate equation approach to Laser theory, stationary solution, time-dependent solution, Gain, loss and

saturation parameters, lasing condition.

Ray and wave propagation in optical media. Matrix formulation of Geometrical optics. Wave reflection

and transmission at a dielectric interface. Diffraction optics in paraxial approximation.

Passive optical resonators, plane-parallel (Fabry-Perot) resonator, concentric, confocal, generalized

spherical and ring resonator. Eigen-modes and Eigen-values. Stability condition, unstable resonator,

photon lifetime and cavity Q.

Q-switching, electro-optical, and acousto-optic Q-switches, saturable absorber Q-switch.

Theory of mode-locking, active and passive mode-locking.

Laser excitation techniques, optical, electrical, and chemical pumping, laser pumping, excitation

transfer, meta-stable states and lifetimes.

Types of lasers, solid-state, dye and semiconductor lasers, gas, chemical, free electron, and X-ray lasers,

laser applications.



Recommended texts:

Principles of Lasers, by Orazio Svelto, publisher: Plenum Press; 4th Edition, (1998).

Laser Fundamentals, by William T. Silfvast, publisher: Cambridge University Press, (2004).

PH-505 Introduction to Quantum Information and Computation

Introduction and overview, history of quantum information and computation, quantum bit,

entanglement, example of EPR or Bell states

Quantum computation: Single and multiple qubit gates, quantum circuits, quantum copying circuit

Quantum teleportation and superdense coding

The density operator: ensemble of quantum states, general properties of density operator, reduced

density operator, postulates of quantum mechanics in density operator formulism

Schmidt decomposition and purification

Entropy and information: Shannon entropy, basic properties of entropy, binary entropy, relative

entropy, conditional entropy and mutual information, von-Neuman entropy and its basic properties

References:

Quantum Computation and Quantum Information, M.A. Nielson and I.I Chuang, Cambridge UniversityPress (2000)

Approaching Quantum Computing, D.C. Marinescu and G.M. Marinescu, Pearson Prentice Hall (2005)

Recommended texts:

Quantum Computation and Quantum Information, Michael A. Nielson and Issac L. Chuang (Cambridge,

2000).

Elements of Information Theory, by J. A. Thomas and T. M. Cover, publisher: Wiley Series (2006).

The Physics of quantum information, by A. K. Bouwmeester, A. Ekert and D. Zeilinger, publisher:

Springer, 1st Edition (2000).

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