J&K Assistant Professor (Physics)
Jammu and Kashmir Public Service Commission - written examination syllabus for Assistant Professor in Physics.
Syllabus for written examination for the Post of Assistant Professor in the subject of Physics I. Mathematical Methods of Physics Dimensional analysis; Vector algebra and vector calculus; Linear algebra, matrices, Cayley Hamilton theorem, eigenvalue problems; Linear differential equations; Special functions (Hermite, Bessel, Laguerre and Legendre);
Fourier series, Fourier and Laplace transforms; Elements of complex analysis: Laurent series - poles, residues and evaluation of integrals; Elementary ideas about tensors. Functions of a complex variable, Cauchy Riemann equations, Harmonic functions, complex integration, Cauchy's integral formula.
II. Classical Mechanics Newton's laws; Phase space dynamics, stability analysis; Central-force motion; Two-body collisions, scattering in laboratory and centre-of-mass frames; Rigid body dynamics, moment of inertia tensor, non-inertial frames and pseudoforces; Variational principle, Lagrangian and Hamiltonian formalisms and equations of motion; Poisson brackets and canonical transformations; Symmetry, invariance and conservation laws, cyclic coordinates; Periodic motion, small oscillations and normal modes. Hamilton-Jacobi equations for Hamilton's characteristic function.
III. Electromagnetic Theory Electrostatics: Gauss' Law and its applications; Laplace and Poisson equations, boundary value problems, 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; Dispersion relations in plasma; Lorentz invariance of Maxwell's equations; Transmission lines and wave guides; Dynamics of charged particles in static and uniform electromagnetic fields; Radiation from moving charges, dipoles and retarded potentials, Lienard-Wiechert potentials.
IV. Quantum Mechanics Wave-particle duality, Wave functions in coordinate and momentum representations; Commutators and Heisenberg's uncertainty principle, Matrix representation; Dirac's bra and ket notation; Schrodinger 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 applications; Variational method; WKB approximation; Time dependent perturbation theory;
Fermi's Golden Rule; Selection rules; Semi-classical theory of radiation; Elementary ideas of relativistic quantum mechanics; Klein Gordon and Dirac equations; Identical particles, Pauli's exclusion principle, spin-statistics connection.
V. Thermodynamic and Statistical Physics Phase space, micro- and macro-states, ensembles: microcanonical, canonical and grand canonical ensembles and partition functions; Free Energy and connection with thermodynamic quantities; Gibb's paradox. First- and second-order phase transitions, Mean field theory, Landau's theory. Classical and quantum statistics, ideal Fermi and Bose gases; Blackbody radiation and Planck’s distribution law; Bose-Einstein condensation; Diffusion equation.
VI. Electronics Semiconductor device physics, including diodes, junctions, transistors, field effect devices, homo and heterojunction devices, device characteristics, frequency and power dependence. Opto-electronic devices, high-frequency devices, Operational amplifiers and their applications; Digital techniques and applications (registers, counters, and similar circuits); A/D and D/A converters. Logic gates; one bit RS, JK, JK-slave, D and T Flip Flops.
VII. Computational methods in physics Numerical analysis: Elements of computational techniques; interpolation and extrapolation, curve fitting, solutions of equations; Bisection method, secant method, numerical integration; Trapezoidal, Simpson's methods, Runge-Kutta method. Solutions of algebraic and transcendental equations; Newton-Raphson method, solution of linear system of equations by Gauss Elimination method.
VIII. Atomic & Molecular Physics Quantum states of an electron in an atom; Electron spin: one electron atoms, Relativistic corrections for energy levels of hydrogen; Hyperfine structure and isotopic shift; width of spectral lines; LS & JJ coupling; Zeeman, Paschen Back & Stark effect; X-ray spectroscopy; Electron spin resonance, Nuclear magnetic resonance, chemical shifts, rotational, vibrational, electronic and Raman spectra of diatomic molecules, selection rules, Frank - Condon principle, spontaneous and stimulated emission, Einstein A & B coefficients.
IX. 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; Drude and Sommerfeld theory, Hall effect and thermoelectric power; Di and paramagnetism, diamagnetism of free electrons and Landau levels; Weiss theory of ferromagnetism and antiferromagnetism; ferroelectricity; 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.
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