Note :-

1. Duration of Paper: 3 Hours
2. All Questions carry equal marks.
3. Medium of Competitive Exam: Bilingual in English & Hindi
4. There will be Negative Marking.
5. Objective type paper .

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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, eigen value 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. Kepler's laws, Gravitational field and potentials
5. Two-body collisions, scattering in laboratory and centre-of-mass frames
6. Rigid body dynamics, Angular momentum, moment of inertia tensor, non-inertial frames and pseudoforces
7. Variational principle, Lagrangian and Hamiltonian formalisms and equations of motion
8. Poisson brackets and canonical transformations
9. Symmetry, invariance and conservation laws, cyclic coordinates
10. Periodic motion, small oscillations and normal modes
11. Damped harmonic oscillations, Driven harmonic oscillations
12. Waves in media, Superposition of waves
13. Special theory of relativity, Lorentz transformations, relativistic kinematics and mass-energy equivalence
14. Kinematics of moving fluids: Bernouli's theorem, Viscosity, Surface tension

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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. Eigen value 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
3. Production of low temperature and its applications
4. Maxwell relations
5. Chemical potential, phase equilibria
6. Phase space, micro- and macro-states
7. Micro canonical, canonical and grand-canonical ensembles and partition functions
8. Free Energy and connection with thermodynamic quantities
9. First and second-order phase transitions
10. Classical and quantum statistics, ideal Fermi and Bose gases
11. Principle of detailed balance
12. Blackbody radiation and Planck's distribution law
13. Bose-Einstein condensation
14. Random walk and Brownian motion
15. Introduction to non-equilibrium processes
16. 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. Particle accelerators and detectors