Exam Scheme

Note :-

1. Objective type paper.
2. All questions carry equal marks.
3. There will be Negative Marking.

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Syllabus : Physics-II

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1. Mathematical Methods of Physics
   1. Dimensional analysis
   2. Vector algebra and vector calculus
   3. Linear algebra, matrices, Cayley Hamilton theorem, eigenvalue problems
   4. Linear differential equations
   5. Special functions (Hermite, Bessel, Laguerre and Legendre)
   6. Fourier series, Fourier and Laplace transforms
   7. Elements of complex analysis
   8. Elementary ideas about tensors
   9. Introductory group theory
   10. Elements of computational techniques: roots of functions, interpolation, extrapolation, integration by trapezoid and Simpson's rule, solution of first order differential equations using Runge-Kutta method
   11. Finite difference methods
   12. Elementary probability theory, random variables, binomial, Poisson and normal distributions.

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2. Classical Mechanics
   1. Newton's laws
   2. Phase space dynamics, stability analysis
   3. Central-force motion
   4. Two-body collisions, scattering in laboratory and centre-of-mass frames
   5. Rigid body dynamics, moment of inertia tensor, non-inertial frames and pseudoforces
   6. Variational principle, Lagrangian and Hamiltonian formalisms and equations of motion
   7. Poisson brackets and canonical transformations
   8. Symmetry, invariance and conservation laws, cyclic coordinates
   9. Periodic motion, small oscillations and normal modes
   10. Special theory of relativity, Lorentz transformations, relativistic kinematics and mass-energy equivalence.

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3. Quantum Mechanics
   1. Wave-particle duality
   2. Wave functions in coordinate and momentum representations
   3. Commutators and Heisenberg's uncertainty principle
   4. Matrix representation
   5. Dirac's bra and ket notation
   6. Schroedinger equation (time-dependent and time-independent)
   7. Eigenvalue problems such as particle-in-a-box, harmonic oscillator, etc.
   8. Tunneling through a barrier
   9. Motion in a central potential
   10. Orbital angular momentum, Angular momentum algebra, spin
   11. Addition of angular momenta
   12. Hydrogen atom, spin-orbit coupling, fine structure
   13. Time-independent perturbation theory and applications
   14. Variational method
   15. WKB approximation
   16. Time dependent perturbation theory and Fermi's Golden Rule
   17. Selection rules
   18. Semi-classical theory of radiation
   19. Elementary theory of scattering, phase shifts, partial waves, Born approximation
   20. Identical particles, Pauli's exclusion principle, spin-statistics connection
   21. Relativistic quantum mechanics: Klein Gordon and Dirac equations.

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4. Thermodynamic and Statistical Physics
   1. Laws of thermodynamics and their consequences
   2. Thermodynamic potentials, Maxwell relations
   3. Chemical potential, phase equilibria
   4. Phase space, micro- and macrostates
   5. Microcanonical, canonical and grand-canonical ensembles and partition functions
   6. Free Energy and connection with thermodynamic quantities
   7. First- and second-order phase transitions
   8. Classical and quantum statistics, ideal Fermi and Bose gases
   9. Principle of detailed balance
   10. Blackbody radiation and Planck's distribution law
   11. Bose-Einstein condensation
   12. Random walk and Brownian motion
   13. Introduction to nonequilibrium processes
   14. Diffusion equation.

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5. Nuclear and Particle Physics
   1. Basic nuclear properties: size, shape, charge distribution, spin and parity
   2. Binding energy, semi-empirical mass formula
   3. Liquid drop model
   4. Fission and fusion
   5. Nature of the nuclear force, form of nucleon-nucleon potential
   6. Charge-independence and charge-symmetry of nuclear forces
   7. Isospin
   8. Deuteron problem
   9. Evidence of shell structure, single- particle shell model, its validity and limitations
   10. Rotational spectra
   11. Elementary ideas of alpha, beta and gamma decays and their selection rules
   12. Nuclear reactions, reaction mechanisms, compound nuclei and direct reactions
   13. Classification of fundamental forces
   14. Elementary particles (quarks, baryons, mesons, leptons)
   15. Spin and parity assignments, isospin, strangeness
   16. Gell-Mann-Nishijima formula
   17. C, P, and T invariance and applications of symmetry arguments to particle reactions, parity non-conservation in weak interaction
   18. Relativistic kinematics.