UPHESC PHYSICS SYLLABUS

1.Mathematical Methods of Physics

Dimensional analysis Vector, algebra and vector calculus, Linear algebra, matrices, CayleyHamilton Theorem

Eigenvalue problems

Linear differential equations

Special functions (Hermite, Bessel, Laguerre and Legendre)

Recurrence relations, Fourier series, Fourier and Laplace transforms

Elements of complex analysis: Laurent series-poles, residues and evaluation of integrals

Elementary ideas about thesors

Introductory group theory, SU(2), O(3)

Elements of computational techniques: roots of functions, interpolation, extrapolation, integration by trapezoid and Simpson’s rule, solution of first order differential equations using Runge-Kutta method

Finite difference methods

Elementary probability theory, random variables, binomial, Poisson and normal distributions

2.Classical Mechanics

Newton’s laws

Phase space dynamics, stability analysis

Central-force motion

Two-body collisions, scattering in laboratory and center-of-mass frames

Rigid body dynamics, moment of inertia tensor, Non-inertial frames and pseudoforces

Variational principle, Lagrangian and Hamiltonian formalism and equations of motion

Poisson brackets and canonical transformations

Symmetry, invariance and conservation laws, cyclic coordinates

Periodic motion, small oscillations and normal modes

Special theory of relativity, Lorentz transformations, relativistic kinematics and mass–energy equivalence

Twin Paradox, Hamilton – Jacobi Theory

3.Electromagnetic Theory

Electrostatics: Gauss’s law and its applications

Laplace and Poisson equations, boundary value problems

Magnetostatics: Biot-Savart law, Ampere's theorem, electromagnetic induction

Maxwell's equations in free space and linear isotropic media

boundary conditions on fields at interfaces

Scalar and vector potentials

Gauge invariance

Electromagnetic waves in free space, dielectrics, and conductors

Reflection and refraction, polarization, Fresnel’s law, interference, coherence, and diffraction

Dispersion relations in plasma

Lorentz invariance of Maxwell’s equations

Transmission lines and wave guides

Cavity Resonator, Dynamics of charged particles in static and uniform electromagnetic fields

Radiation from moving charges, dipoles and retarded potentials Plasma

4.Quantum Mechanics

Wave-particle duality

Wave function in coordinate and momentum representations

Commutators and Heisenberg’s uncertainty principle

Matrix representation

Dirac’s bra and ket notation

Schroedinger equation (time-dependent and time-independent)

Eigenvalue problems such as particle-in-a-box, harmonic oscillator, etc.

Tunneling through a barrier

Motion in a central potential

Orbital angular momentum, Angular momentum algebra, spin

Addition of angular momenta

Hydrogen atom, spin-orbit coupling, fine structure

Time-independent perturbation theory and Time dependent perturbation theory and Fermi's Golden Rule

Selection rules

Semi-classical theory of radiation

Elementary theory of scattering, phase shifts, partial waves, Born approximation

Identical particles, Pauli’s exclusion principle, spin-statistics connection

Relativistic quantum mechanics: Klein Gordon and Dirac equations

5.Thermodynamic and Statistical Physics

Laws of thermodynamics and their consequences

Thermodynamic potentials, Maxwell relations

Chemical potential, phase equilibria

Phase space, micro- and macrostates

Microcanonical, canonical and grand-canonical ensembles and partition functions

Free Energy and connection with thermodynamic quantities

First- and second-order phase transition

Classical and quantum statistics, ideal Fermi and Bose gases

Principle of detailed balance

Blackbody radiation and Planck’s distribution law

Bose-Einstein condensation

Random walk and Brownian motion

Introduction to non equilibrium processes

Diffusion equation

6. Electronics

Semiconductor device physics, including diodes, junctions, transistors, field effect devices, homo and heterojunction devices, device structure, device characteristics, frequency dependence and applications

Optoelectronic devices, including solar cells, photodetectors and LEDs

Highfrequency devices, including generators and detectors

Operational amplifiers and their applications

Digital techniques and applications (registers, counters, comparators and similar circuits)

A/D and D/A converters

Microprocessor and microcontroller basics

Oscillator, Amplifier, Modulation & demodulation, Switching time, High frequency devices

7. Experimental Techniques and data analysis

Data interpretation and analysis

Precision and accuracy, error analysis, propagation of errors, least squares fitting, linear and nonlinear curve fitting, chi-square test

Transducers (temperature, pressure/vacuum, magnetic field, vibration, optical, and particle detectors), measurement and control

Signal conditioning and recovery, impedance matching, amplification (Op-amp based, instrumentation amp, feedback), filtering and noise reduction, shielding and grounding

Fourier transforms

lock-in detector, box-car integrator, modulation techniques

Application of experimental and analytical techniques

8. Atomic & Molecular Physics

Quantum states of an electron in an atom

Electron spin

Stern-Gerlach experiment

Spectrum of Hydrogen, helium and alkali atoms

Relativistic corrections for energy levels of hydrogen

Hyperfine structure and isotopic shif

width of spectral lines

LS & JJ couplings

Zeeman, Paschen Bach & Stark effect

X-ray spectroscopy

Electron spin resonance, Nuclear magnetic resonance, chemical shif

Rotational, vibrational, electronic, and Raman spectra of diatomic molecules

Frank - Condon principle and selection rules

Spontaneous and stimulated emission, Einstein A & B coefficients

Lasers, optical pumping, population inversion, rate equation

Modes of resonators and coherence length, U-V and infrared spectrometry

9. Condensed Matter Physics

Bravais lattices; Reciprocal lattice, diffraction and the structure factor

Bonding of solids

Elastic properties, phonons, lattice specific heat

Free electron theory and electronic specific heat

Response and relaxation phenomena

Drude model of electrical and thermal conductivity

Hall effect and thermoelectric power

Diamagnetism, paramagnetism, and ferromagnetism

Electron motion in a periodic potential, band theory of solids, Superconductivity: type-I and type-II superconductors

Josephson junctions

Defects and dislocations

Ordered phases of matter, translational and orientational order, kinds of liquid crystalline order

Conducting polymers

Quasicrystals, Quantum Hall effect

10. Nuclear and Particle Physics

Basic nuclear properties: size, shape and charge distribution, spin and parity

Binding energy, semiempirical mass formula

Liquid drop model

Fission and fusion

Nature of the nuclear force, form of nucleon-nucleon potential

Charge-independence and charge-symmetry of nuclear forces

Isospin

Deuteron problem

Evidence of shell structure, single-particle shell model, its validity and limitations

Rotational spectra

Elementary ideas of alpha, beta and gamma decays and their selection rules

Nuclear reactions, reaction mechanisms, compound nuclei and direct reactions

Classification of fundamental forces

Elementary particles (quarks, baryons, mesons, leptons)

Spin and parity assignments, isospin, strangeness

Gell-Mann- Nishijima formula

C,P, and T invariance and application of symmetry arguments to particle reactions, parity non-conservation in weak interaction; Relativistic kinematics