PG TRB Physics
Master the laws of the universe with the well-structured PG TRB Physics syllabus.
It features Mechanics, Thermodynamics, Electromagnetism, Quantum Physics, and Solid State Physics.
At Professor Academy, our expert mentors break down tough concepts for deeper understanding. Explore the complete PG TRB Physics syllabus today and start learning with clarity.
PG TRB Physics Syllabus
Unit I – MATHEMATICAL PHYSICS
Dimensional analysis: Differential equation (ordinary and partial) – order of equation – Expressions for gradient, divergence, curl and Laplacian – vector algebra and vector calculus – Gauss divergence theorem – Green’s theorem – Stokes’ theorem. Matrix: Cayley – Hamilton theorem, inverse of matrix – Eigen values and Eigen vectors. Polynomials: Hermite, Bessel and Legendre Functions. Special function: Beta and Gamma functions. Probability: Elementary probability theory – Random variables – Binomial – Poisson and Normal distribution. Complex variables: Analytic functions – Singular points – Cauchy’s integral theorem and formula -Taylor’s and Laurent’s expansions, poles, Calculus of residues and evaluation of integrals. Integral transforms: Fourier series and Fourier transform and their properties.
Unit II – CLASSICAL MECHANICS
Mechanics of particles and systems of particles: Constraints and Generalized coordinates, Law of conservation of Energy, Linear and Angular momentum, Conservative and Non-Conservative systems, Degrees of freedom, Holonomic – Nonholonomic – Scleronomic systems. Lagrangian Formalism: Lagrange equations of motion – D’Alembert’s principle – Applications (Simple pendulum, Atwood’s machine, Harmonic Oscillator, Electrical circuit). Hamiltonian Formalism: Hamilton’s equation of motion – Cyclic co-ordinates – Hamilton’s equation from variational principle, Principle of least action, Canonical transformation, Liouville’s theorem. Rigid body Dynamics: Euler’s angles – Moment of inertia tensor, Euler’s equation of motion – Symmetrical top, Special theory of Relativity: Inertial and Non- inertial frames, Lorentz transformation, Lorentz inverse transformation, Length contraction, Time dilation, Mass invariance, Einstein’s mass-energy relation.
Unit III – ELECTROMAGNETIC THEORY
Electrostatics: Coulomb’s law – Gauss’s law and its application. Laplace and Poisson’s equations. Magnetostatics: Biot Savart’s law – Ampere’s law – Magnetic scalar and vector potentials – magnetic susceptibility – Equation of continuity – Displacement current – Maxwell’s equations (free space and linear isotropic media) – Electromagnetic waves – Poynting’s theorem – Dielectrics: Retarded potentials – Polarization – Radiation from a linear antenna – Transmission lines and Wave guides.
Unit IV – QUANTUM MECHANICS
Failures of Classical mechanics – Black body radiation – Wave and particle duality – Postulates of Quantum mechanics – Wave function and properties – Expectation values – Heisenberg’s uncertainty principle – Schrodinger equations (time – dependent and time- independent). Eigen value problems: Particle in a box (1D and 3D), Particle in a finite potential well & barrier, Tunnelling, Harmonic oscillator. Operators: Ladder operators, Angular momentum operator, Hydrogen atom, spin – Stern Gerlach experiment. Approximation methods: Variational principle, Time independent (1st and 2nd order ) degenerate and non-degenerate perturbation theory – Time-Dependent perturbation theory – Fermi’s golden rule, Identical particles. Relativistic Quantum Mechanism: Pauli’s spin Matrices, Dirac and Klein Gordon equation. Commutators. Scattering theory: Scattering cross-section, Scattering by a central potential, Partial wave analysis, Breit-Wigner formula.
Unit V – THERMODYNAMICS AND STATISTICAL MECHANICS
Laws of thermodynamics and their consequences – thermodynamic system (closed and open) – thermodynamic processes (isothermal, adiabatic, isochoric, isobaric, isotropic) – cyclic process – thermodynamic potentials (U, S, G, H) – relation between them. Specific heat – equation of state – intensive and extensive variables – The P-V diagram – Carnot cycle and its efficiency – Entropy – reversible and irreversible – T-S diagram – Equipartition theorem. Phase space – micro and macrostates – Liouville’s theorem – ensembles – partition function – classical (MB distribution) – Maxwell’s distribution of velocities – Kinetic Theory of gases – Pressure exerted by gas – Mean free path – Mean – RMS and most probable speed – and quantum (BE & FD distribution) statistics – applications to black body radiation – Bose Einstein condensation.
Unit VI – ATOMIC PHYSICS AND SPECTROSCOPY
Quantum states of an electron in an atom – Hydrogen atom spectrum – Electron spin -Spin orbit coupling – Fine structure – Relativistic correction – Spectroscopic terms and selection rules – Hyperfine structure – Exchange symmetry of wave functions – Pauli’s exclusion principle – Hund’s rule – Periodic table – Alkali type spectra – LS and JJ Coupling – Zeeman, Paschen – Back and Stark effects. Principles of ESR, NMR, Chemical shift – Frank Condon principle – Born Oppenheimer approximation – Electronic, rotational and vibrational spectra of diatomic molecules, Selection rules.
Unit VII – SOLID STATE PHYSICS
Crystal Physics: Lattice, Crystal structures – Bravais lattices – Miller indices – Reciprocal lattices – Lattice Dynamics: Monoatomic, diatomic lattices – Theories of specific heat – Einstein’s and Debye’s model for lattice specific heat. Classical free electron theory: Drude model – Thermal conductivity – Wiedemann Franz law. Energy bands in solids: Energy bands in metals, insulators and semiconductors, E-k diagram – Density of states – Brillouin zones – Wave equation of electron in a Periodic potential. Semiconductor Physics: Types of semiconductors – Mobility – Carrier concentration of charge carriers – Bloch’s theorem – Kronig – Penney model. Dielectrics: Polarization Mechanism – Clausius – Mossotti Equation – Piezo, Pyro and Ferroelectricity. Magnetism: Dia, Para, Ferro, Anti-Ferro and Ferri magnetism. Superconductivity: Meissner effect – Type I and Type II superconductivity – BCS theory – Josephson effect.
Unit VIII – NUCLEAR AND PARTICLE PHYSICS
Nuclear properties (size, shape, charge distribution, spin and parity) – Binding energy, Nuclear force – Liquid drop model – semi – empirical mass formula, Shell model and Collective model – Deuteron, Ground state of deuteron – exicted state of deuteron – Meson theory of nuclear force – Yukawa potentials – Elementary ideas of alpha, beta and gamma decays – Radioactive decay – Fission, Fusion – Chain reaction – Nuclear reactor. Elementary particles: Classification of elementary particles, Fundamental interactions (EM, Strong, Weak, Gravitational) and their quantum numbers (charge, spin, parity, isospin, strangeness, etc.) – Gell-Mann- Nishijima formula. Elementary particles – Classifications – Quark model, Baryons and Mesons, Parity non-conservation in weak interaction.
Unit IX – ELECTRONICS
Semiconducting devices: Diodes – Junction diode – Rectification – Zener diode – Light Emitting Diode. Junction Transistors: common base, common emitter and common collector configurations – Static characteristics – Transistors as amplifier and oscillators – FET, JFET, MOSFET. IC: Fabrication technology, Monolithic IC Processing. 555 Timer, Phase shift, Wien bridge oscillators. Operational Amplifier (IC 741): Op-Amp characteristics, Inverting and Non-inverting Amplifiers, Adder, Subtractor, Differentiator and Integrator. Digital techniques and applications: Flip Flops, Registers – Counters. Digital integrated circuits: Logic gates, NAND and NOR – Universal building blocks – Half and Full adder. Communication Electronics: Modulation and Demodulation (AM, FM, Phase), Transmitter and Receiver, Satellite and Fiber optic communication.
Unit X – EXPERIMENTAL PHYSICS
Units and dimension of physical quantities – significant figures. Data interpretation and analysis, precision and accuracy, error analysis, propagation of errors, Least square fitting. Measurement of fundamental constants – e, h, c – Detection of X-rays, gamma rays, Charged particles, neutrons. Ionization chamber – proportional counter – Measurement of e/m ratio – Measurement of Hall voltage, mobility and charge carrier concentration – measurement of resistance and capacitance in series and parallel.
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