TRB Lecturers in Government Polytechnic Colleges Physics Syllabus 2017. This is the final syllabus and remember it is enough to read just this portion to write TRB exam for Lecturers in Govt Polytechnic Colleges. PHYSICS UNIT 1: MATHEMATICAL METHODS Differential Equations: recurrence formulae for Jn(x) - generating function for Jn(x) Hermite differential equation Hermite's polynomials – Generating function of Hermite polynomials Recurrence formulae for Hermite polynomials - Rodrigue's formula – Complex variables: analytic function - C-R differential equations - C-R equations in polar form –Laplace’s equation – examples - Cauchy's integral Theorem and formula - Taylor's series - Laurent's series - Singularities of an analysis function - Residues and their evaluation – Cauchy residue theorem - Evaluation of definite integrals (trigonometric functions of cos θ and sin θ only) Group theory : concept of a group - Abelian group – Generators of finite group - Cyclic groups Group multiplication table - Rearrangement theorem – Sub groups - Lagrange's theorem for finite group conjugate elements and classes - Group of symmetry of an equilateral triangle Group of symmetry of square – Representation of a group – Reducible and irreducible representation - Schur's lemmas - Orthogonality theorem - Tensor, beta and gamma functions: scalars, Contravariant and covariant vectors – Tensors of higher rank – Algebraic operation of tensors - Mixed tensor – Symmetric and anti-symmetric tensors – Quotient law - Beta and Gamma functions : Definitions - Symmetry property of Beta function – Other forms of Beta function - Evaluation of Gamma function – Other forms of Gamma function – Relation between Beta and Gamma functions - Examples. UNIT 2: CLASICAL MECHANICS AND RELATIVITY Lagrangian formulation: Generalized coordinates – Mechanics of a particle and system of particles (momentum and energy) D'Alemberts principle - Lagrange's equations – Applications (linear harmonic oscillator, simple pendulum isotropic oscillator and electrical circuit) Hamilton's equations - Applications (simple pendulum, compound pendulum and 20 harmonic oscillator) – Deduction of Hamilton's principle - Hamilton's variational principle – Principle of Least action. Canonical transformations : Equation of canonical transformations – Infinitesimal contact transformations – Lagrange and Poisson brackets as Canonical invariants – Equations of motion in Poisson bracket form - Jacobi's identity – Relation between Lagrange and Poisson brackets – Action angle variables - Euler's angles – Angular velocity of a rigid body - Euler's equation of motion – Relativity : Einstein's Mass – Energy relation – Relation between momentum and energy – Four vectors – Four velocity – Energy – Momentum four vectors – Four force Relativistic classification of particles – Relativistic Lagrangian, Hamilltonian function relativistic Lagrangian Hamiltonian of a charged particle in an E.M field. UNIT 3: QUANTUM THEORY AND ITS APPLICATIONS General Principles of Quantum Mechanics: Wave packet – Time dependent and time independent Schrodinger equation - Linear vector space – Linear operator - Eigen function and Eigen values - Hermitian operator – Postulates of Quantum Mechanics – Simultaneous measurability of observables – General uncertainty relation - Dirac's notation – Applications : Square well potential with rigid walls and finite walls - Square potential barrier - Alpha emission – Bloch waves in a periodic potential – Kronig - Penny square-well periodic potential Linear harmonic oscillator: Schrodinger method - Operator method - Delta function - Particle moving in a spherically symmetric potential - System of two interacting particles – Rigid rotator Hydrogen atom - Hydrogen orbitals - Angular Momentum : The angular momentum operators Spin vectors for Spin-(1/2) system – Addition of angular momenta - Time independent and dependent Perturbation theory – Basic concepts – Non degenerate energy levels – Anharmonic oscillator: First-order correction – Ground state of Helium – Effect of electric field on the ground state of hydrogen - Transitions to continuum states – Absorption and emission radiation Einstein's A and B coefficients - Selection rules – Theory of Scattering : Scattering cross- section Scattering by a central potential : partial wave analysis - Significant number of partial waves Scattering by an attractive square - well potential - Breit-Wiger formula – Scattering length Expression for phase shifts – Integral equation – The Born approximation – Scattering by screened Coulomb potential - Validity of Born approximation – Laboratory and centre of mass co-ordinate system UNIT 4: ELECTROMAGNETIC THEORY Electrostatics – Electric charge – electric charge density - Coulomb's law – Electric intensity -Electric potential – Gauss law- Applications – Boundary value problems in electrostatics – Methods of separation variables in Cartesian co-ordinates. Magneto statics - Ampere's circuital law - Magnetic scalar potential – Magnetic vector potential – Magnetization and Magnetization current – Magnetic intensity – Magnetic susceptibility. Equation of continuity – Displacement current - Maxwell's equation – Derivations – energy in electromagnetic fields - (poynting's theorem). Maxwell's equation in terms of electromagnetic potentials – Concept of gauge-Lorentz gauge. Plane electromagnetic wave and their propagation – Interaction of electromagnetic wave with matter on microscopic scale. Retarded potentials - Radiation from a linear antenna. UNIT 5: THERMODYNAMICS AND STATISTICAL MECHANICS Thermodynamics as phenomenological science – Thermodynamic systems - Closed, open, isolated systems – Thermodynamic processes - Adiabatic, isothermal, isochoric, isobaric, isentropic, cyclical and free expansion processes - Reversible, irreversible and Quasi-static processes – Equation of state – Intensive and extensive variables - The PV diagram. Conversion of work into heat and vice-versa – Efficiency - Kelvin-Planck statement of the second law of thermodynamics – Clausius statement of the second law – Carnot cycle – Carnot refrigerator - Carnot's theorem and corollary. Equation of state of a gas from Avogadro's law – Ideal gas equation – Specific heat, internal energy and enthalpy of an ideal gas – Entropy change of an ideal gas – Reversible adiabatic process - Reversible isothermal process. Concept of entropy – Entropy of an ideal gas – The TS diagram - Entropy, reversibility and irreversibility. Microstate and Macrostate of macroscopic system, Phase space and Phase space density, Liouville theorem. Canonical ensemble canonical partition function. – Grand canonical ensemble - Density operator, Spin statistics connection, Grand partition function for ideal Bose and Fermi gases, Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann distributions, Application to Black body radiation: Bose theory(a) Debye theory of specific heat(b) Bose-Einstein condensation – Phase transitions. UNIT 6: Atomic and Molecular Physics Electromagnetic spectrum – Absorption or Emission of radiation - Line width - Natural line broadening – Doppler broadening – Pressure broadening - Removal of line broadening - X-ray Spectra – Emission and absorption spectra of X-rays. Regular and irregular doublet laws - X-ray satellites – Photoelectron spectroscopy - Ultraviolet photoelectron spectrometers – XPS techniques and Chemical information from photoelectron spectroscopy – Auger electron spectroscopy. Infrared Spectroscopy – Vibrational Energy of a Diatomic molecule - The Diatomic Vibrating Rotator - The Vibrations of Polyatomic molecules – Rotation – Vibration spectra of Polyatomic molecules – Analysis by Infra-red Techniques – IR spectrophotometer Fourier Transform - IR spectrophotometer – Applications - Frank-Condon principle and dissociation energy. Raman Spectroscopy – Theories of Raman scattering – Rotational Raman Spectra – Vibrational Raman Spectra – Mutual Exclusion principle – Raman Spectrometer Polarization of Raman Scattered light – Structural determination from Raman and IR spectroscopy - Near IR – FT- Raman spectroscopy. Laser Spectroscopy - Basic principles: Comparison between conventional light sources and lasers – Saturation - Excitation methods – Detection methods – Laser Wavelength Setting – Doppler Limited Techniques. Nuclear Magnetic Resonance Spectroscopy - Basic principles – Magnetic resonance – Relaxation processes – Pulsed (Fourier Transform) NMR - Wide line NMR spectrometers – Spectra and molecular structure – Chemical shifts - Spin-spin coupling – Integration - Applications. - Principles of Mossbauer spectroscopy – Chemical shifts – Quadrupole splitting and Zeeman splitting. Applications of Mossbauer spectroscopy.