Physics Syllabus for SSB Odisha
Unit – I : Mathematical Physics and Classical Mechanics
- Vector calculus and complex variable :
Vector Calculus, Gauss theorem and Stokes theorem.
Cauchy’s theorem, Cauchy’s integral formula, classification of singularities,branch point and
branch cut, Residue theorem, evaluation of integral using residue theorem.
- Special functions :
Basic properties and solutions (series expansion, recurrence and orthogonality relations) of
Bessel, Legendre, Hermite, Beta and Gamma function, Fourier Series , Dirac delta function,
Laplace and Fourier trans form.
- Hamilton’s principle:
Hamilton’s principle, Lagrange’s equation from Hamilton’s principle, Solution of Lagrange
equation of motion for Simple harmonic oscillator. Hamilton’s
equations of motion, canonical equations from variational principle, principle of least action
- Canonical transformation:
Generating function and Legendre transformation, Lagrange and Poisson’s brackets,
conservation theorems in Poisson bracket formalism, JacobiIdentity.
- Coupled oscillations:
Theory of coupled oscillation, Normal modes, Energy relation and transfer
Unit – II : Classical Electrodynamics
- Electrostatics and Magnetostatics:
Scalar and vector potential, Gauge transformation, multipole expansion of
- Scalar potential
and electrostatic energy due to static charge distribution,
- Vector potential due to stationary
current distribution, Electrostatic andmagnetostatic energy, Poynting’s theorem.
- Maxwell’s electromagnetic equations-wave equation in conducting medium. Reflection of
electromagnetic waves (normal and oblique incidence) from
- Dielectric and
- Metallic
interface.
- Relativistic electrodynamics:
Equation of motion in an electromagnetic field, electromagnetic field tensor,covariance of
Maxwell’s equation, Maxwell’s equations as equations ofmotion, Lorentz transformation laws
for electromagnetic field, and the fieldsdue to point charge in uniform motion.
- Radiation, scattering and diffraction:
Field due to localized oscillating source, electric dipole, magnetic dipole,electric quadrupole
field radiation, centre-fed linear antenna with sinusoidalcurrent, scattering by a small dielectric
sphere in long wave length limit,Raleigh scattering,
- Growth and decay of current in dc circuit containing LR, CR and LCR. Alternating current
circuits containing LR, CR and LCR – Resonance.
Unit – III : Quantum Mechanics
- Wave packet: and Schrödinger’s equation.
Gaussian wave packet, spreading of wave packet, Schrödinger’s equation, probability
interpretation of wave function, expectation values,coordinate and momentumrepresentation, x
and p in these representations, stationary states, Eigen states, Ehrenfest theorem, Quontumvirial
theorem. Linear independence and Linear dependence, Expansion Theorem, Ortho-normality
and Completeness conditions.
- Operator method in Quantum Mechanics: operator algebra, Eigen function and eisen values
of Hermitian operator,Formulation of Quantum Mechanics in vector space language,
uncertaintyproduct of twonon commutingHermitian operators, one dimensional harmonic
oscillator Matrix representation of operators, Schrodinger, Heisenberg and interactionpictures.
Potential well (Finite, infinite ) in one dimension, potential step.
- Angular momentum:
Angular momentum algebra, addition of two angular momenta j_1=1/2,j_2=1/2. Clebsch–
Gordon Coefficients, examples, matrix representation ofj_1=1/2 and j_2=1. Spin angular
momentum, Pauli spin matrices and theirproperties, eigen value and eigen function,
- Radial solution of Hydrogenatom and its wave function in ground state.
- Approximation methods:
Time independent perturbation theory, First and second order correction toenergy and eigen
functions, application toone electron system, Zeemaneffect, linear Stark effect.
Unit – IV : Condensed matter Physics, Statistical Mechanics and Electronics
- Classical Statistical Mechanics:
Microstates, macro states, phase space, Liouville’s theorem, concept ofensembles, Ergodic
hypothesis, postulates of equal a priory probability,Boltzmann’s postulates of entropy, micro
canonical ensemble, entropy of idealgas, Gibb’s paradox.
Canonical ensemble:
Expression for entropy, canonical partition function, Helmholtz free energy,energy fluctuation,
Max well Boltzmann distribution law.
- Digital Circuits
Logic fundamentals, Boolean theorem, Logic gates-RTL,DTL,TTL, RS flipflop, JK flip-flops
Boolean algebra, De Morgan theorem, AND, NAND, NOT, NOR gates Logic Circuits.
- Lattice Dynamics:
Classical theory of lattice vibration under harmonic approximation, vibration oflinear mono
atomic and diatomic lattices, acoustical and optical modes, opticalproperties of ionic crystal in
the infrared region, normal modes and phonon,inelastic scattering of neutron by phonon, lattice
heat capacity, models of Debye and Einstein.
Free Electron Theory:
Free electron theory of metal,one dimensional infinite potential well. Electrongas in three
dimension, density of states, electronic specific heat, electrical conductivity and WiedemanFranz
law, Hall effect, cyclotron resonance.
- Band Theory of Solid:
Nearly free electron model, effective mass of electron in the band, concept of
holes, classification of metal, semiconductor and insulator, intrinsic and
extrinsic semiconductors, intrinsic carrier concentration,
- Magnetic Properties of Solids:
Quantum theory of diamagnetism, paramagnetism, PauliParamagnetism, Ferromagnetism,
Curie-Weiss law.
Unit – V : Nuclear and Particle Physics
- Nuclear Properties:
Basic nuclear properties: nuclear size, nuclear radius and charge distribution,nuclear form
factor, mass and binding energy, Angular momentum, parity Magnetidipole moment and electric
quadrupole moment,
- Two body bound state;
Properties of deuteron, Schrodinger equation and its solution for ground stateof deuteron, rms
radius, spin dependence of nuclear forces, electromagneticmoment and magnetic dipole
moment of deuteron and the necessity of tensorforces.
- Beta-decay :
β- emission and electron capture, Fermi's theory of allowed β-decay, Selectionrules for Fermi
and Gamow-Teller transitions, Parity non-conservation andWu's experiment.
Liquid drop model, Bethe-Weizsacker binding energy/mass formula, Shell model and
Collective model.
- Nuclear Reactions and Fission.
Different types of reactions, Quantum mechanical theory, Resonancescattering and reactions,
Breit-Wigner dispersion relation; Compound nucleusformation and break-up Nuclear fission:
Experimental features, spontaneous fission, liquiddrop model, barrier penetration and Alpha
decay.
- Particle Physics:
Basic forces, classification of elementary particle, Gellmann-Nishijimascheme,meson and
Baryon octet, isospin, strangeness, spin ,parity, Leptonand baryon number conservation, parity
conservation and non conservation ,time reversal and consequence of time reversal invariance,
chargeconjugation, G-parity, Statement of CPT theorem and its consequences,
Hadron classification by isospin and hypercharge, SU(2) Symmetry Groups,algebras and
generators;Elementary idea of SU(3) symmetry and Quarksmodel, need for Color;
