Pg trb syllabus - Physics

Trb syllabus 2021 - Physics

 UNIT- I - Vector Fields 

General expression for gradient, divergence curl and Laplace operators in orthogonal curvilinear Co-ordinates and their explicit form in Cartesion spherical-co-ordinates, Stokes theorem and Gauss theorem. 

Matrix theory 

Algebraic operation – Rank of a matrix. Eigen values and Eigen vectors - characteristic equation – Cayely Hamilton theorem – Diagonalisation and Diagonalizability of 

unitary orthogonal. Hermitian and symmetric matrices. Special functions Legendre, Hermite and Lagune equation basic properties – Gamma and Beta functions. 

UNIT-II - Probability and Theory of errors 

Basic concept of probability distribution – Exclusive events and addition – 

Compound events and products – Binomial – Poisson and Guassian distribution – Normal 

distribution of error – Standard error – Principle of least squares – Application of solution of linear equation – Curve fitting. 

Group theory 

Definition – Sub-groups – Homomorphism and isomorphism – Group representations – Irreducible representation – Unitary representation. 

 UNIT – III - Classical mechanics 

 Generalised co-ordinates – D’Alembert's principle, Lagrangian equation of motion – Hamiltonian equation – Conservative and non-conservative systems - Hamilton equation, 

cyclic variables, principle of least action – Theory of small oscillations – Normal co-ordinates and normal modes - Linear Triatomi molecule - Rigid bodies -Moments and products oclic variables, principle of least action – Theory of small oscillations – Normal co-ordinates 

and normal modes - Linear Triatomi molecule - Rigid bodies -Moments and products of inertia     Euler’s angle - Euler’s equation of motion symmetric top

UNIT-IV - Statistical Mechanics 

Maxwell Boltzmann statistics Maxwellian distribution of velocities – Mean – root Mean square and most probable velocities Bose-Einstein statistics – Distribution function – Phonon gas – Black body radiation – Fermy-Dirac statistics – Distribution function – Electron gas – Pauli paramagnetism – Thermionic emission – Elementary idea of phase transition – 

Properties of liquid Helium – phase space, Liouville’s theorem – statistical equation – micro canonical ensembles – Equation of statethermodynamic functions of an ideal gas equipartition of energy. 

UNIT-V - Electromagnetic theory 

 Coulomb law – Gauss law – Poisson’s equation – Laplace equation and solution to boundry value problem – Electrostatics of dielectric media – Molecular polarisability and its application – Vector – Scalar potential – B and H in a magnetic material – Maxwell’s equations and their significance – Poynting theorem – Radiation of oscillating dipole. 

Relativistic Mechanics 

Basic ideas - Lorentz transformation. Time dilation and Lorentz contraction -Velocity addition law - Momentum and energy in relativistic Mechanics - Centre of mass system for two relativistic particles. 

UNIT-VI - Spectroscopy 

Rotation spectra – Vibration spectra – Rotation vibration spectra of diatomic and linear molecules – Raman Spectra – experimental techniques and classical theory of Raman Scattering – Electronic state of diatomic molecules – Frank–Condon principle – Hund’s coupling scheme – Evaluation of molecular constant from vibrational spectra data. Interaction between nuclear spin and magnetic field – Nuclear resonance-Chemical shift-Dipole-Dipole interactionSpin lattice interaction. 

UNIT-VII - Solid State Physics 

Energy levels and density of states in one, two and three dimensions – Electrical and Thermal conductivities – Wiedmann-Franz law. Energy bands in solids – Transport phenomena in semiconductors operational functions of a junction diode-Schottky diode – Bloch theorem - Krong-Penny mudel – Brillouin zones – Wave equation of an electron in a periodic potential. 

Thermal Properties of solids 

 Laws of Thermodynamics – Maxwell’s relations and their applications – Phase transitions – Production and measurement of low temperatures –Einstein and Debye theory of specific heats of solid. 

Magnetic properties of materials 

 Langevin’s theory of dia-para-magnetism – Quantum theory of para – magnetism – 

Ferro – magnetism – Ferri – magnetism – superconductivity – Meissner effect – 

Thermodynamics of superconducting materials – London equation – B.C.S. theory – Josephson’s 

effect. 

UNIT-VIII - Quantum mechanics 

 Schrodinger’s wave equation – Free particle – Particle in a potential well and barrier penetration - The probability interpretation – Expectation value – Eigen functions and eigen values – Stationery states – Wave packet – Uncertainty principle – Linear Harmonic 

oscillator – angular momentum and addition of angular momenta. Peturbation theory – 

Transition probability – Constant and harmonic perturbation – Scattering theory – Differential 

and total scattering cross section – Born approximation – Partial wave analysis and phase shift analysis – Relativistic wave equations – Klein – Gordon equations – Dirac equation and its free particle solution. 

UNIT-IX - Nuclear Physics 

Binding energy – Semi empirical mass formula – Stability of nuclei – Nuclear forces – Ground state of deuteron – Alpha decay – B decay – Fermi’stheory – Selection rules – Liquid drop model – Nuclear fission – Shell model – Collective models. Nuclear Instrumentation Cyclotron - Synchro cyclotron – Proton synchrotron – Detectors – G.M.Counter – Scintillation Counter – Bubble chamber – Nuclear reactors – Neutron cross section – Fission product – Energy release – Chain reaction – Multiplication factor 

Moderator – Natural Uranium – Diffusion equation. 

Unit X - Electronics (Digital electronics) 

Binary - Decimal – Octal and Hexadecimal numbers – 8421 Excess–3 - Gray Codes – Logic gates – Laws Boolean algebra – Half and full adders – Subtractors – RS, RST, JK and M/S Flip-flops – Ripple counter – Decade counter –Up-down counter – Serial and parallel registers. 

Operational amplifier 

Differential amplifier – Parameters – Applications – Analog integration and 

differentiation – Analog computation – Comparators – Sample and hold circuits – Oscillator – Hartley-Colpitt-Phase Shift - Wien’s bridge oscillators – Astable mono -Bistable multivibrators – Clipping and clamping circuits

Microwave Physics 

Microwave generation – Klystron – Magnetron – Travelling wave tubes – Microwave in rectangular and cylindrical wave guides – Characteristics of Antennas – Short dipole radiation – Antenna gain – Directivity – Radiation resistance – Radiation intensity. 

Microprocessor 

Evolution of Microprocessors – Organisation of micro-computers- Preliminary concepts – Basic concepts of programming – Architecture – Address – Data and control buses – Memory decoding – Memory mapped I/O and I/O mapped I/O. Machine and instruction cycles – 

Addressing modes – Use of arithmetic logical data – Transfer stack and I/O instructions – 

Instruction set and assembly programming of 8085 microprocessor – Fetch – Execute – overlap – 

Instruction cycles – Instruction forward – Memories – RAM-PROMS, EPROMSEEPROMS – 

Static and Dynamic RAM.