Physical Science Syllabus Paper 1 Section B

Physical Science Syllabus Paper 1 Section B

1. Basic Mathematical Methods: Calculus: Vector algebra and vector calculus. Linear algebra, matrices. Linear differential equations. Fourier series, Elementary complex analysis.

2. Classical Dynamics: Basic principles of classical dynamics. Lagrangian and Hamiltonian formalisms. Symmetries and conservation laws. Motion in the central field of force. Collisions and scattering. Mechanics of a system of particles. Small oscillations and normal modes. Wave motion - wave equation, phase velocity, group velocity, dispersion. Special theory of relativity - Lorentz transformations, addition of velocities, mass-energy equivalence.

3. Electromagnetics: Electrostatics - Laplace and Poisson equations, boundary value problems. Magnetostatics - Ampere's theorem, Biot-Savart law, electromagnetic induction. Maxwell's equations in free space and in linear isotropic media. Boundary conditions on the fields at interfaces. Scalar and vector potentials. Gauge invariance. Electromagnetic waves - reflection and refraction, dispersion, interference, coherence, diffraction, polarization. Electrodynamics of a charged particle in electric and magnetic fields. Radiation from moving charges radiation from a dipole. Retarded potential.

4. Quantum Physics and Applications: Wave-particle duality. Heisenberg's uncertainty Principle. The Schrodinger equation Particle in a box, Harmonic Oscillator, Tunnelling through a barrier. Motion in a central potential, Orbital angular momentum. Angular momentum algebra, spin. Addition of angular momenta. Time-independent perturbation theory. Fermi's Golden Rule. Elementary theory of scattering in a central potential. Phase shifts, partial wave analysis, Born approximation, Identical particles, spin-statistics connection.

5. Thermodynamic and Statistical Physics: Laws of thermodynamics and their consequences, Thermodynamic potentials and Maxwell's relations. Chemical potential, phase equilibria. Phase space, microstates and macrostates. Partition function. Free Energy and connection with thermodynamic quantities. Classical and quantum statistics, Degenerate electron gas. Blackbody radiation and Planck's distribution law, Bose-Einstein condensation. Einstein and Debye models for lattice specific heat.

6. Experimental Design: Measurement of fundamental constants: e, h, c. Measurement of High & Low Resistances, L and C. Detection of X-rays, Gamma rays, charged particles, neutrons etc: Ionization chamber, proportional counter, GM counter, Scintillation detectors, Solid State detectors. Emission and Absorption Spectroscopy. Measurement of Magnetic field, Hall effect, magnetoresistance. X-ray and neutron Diffraction. Vacuum Techniques: basic idea of conductance, pumping speed etc. Pumps: Mechanical Pump, Diffusion pump; Gauges: Thermocouple, Penning, Pirani, Hot Cathode. Low Temperature: Cooling a sample over a range upto 4 K and measurement of temperature.

Measurement of Energy and Time using electronic signals from the detectors and associated instrumentation: Signal processing, A/D conversion & multichannel analyzers, Time-of-flight technique; Coincidence Measurements: true to chance ratio, correlation studies. Error Analysis and Hypothesis testing: Propagation of errors, Plotting of Graph, Distributions, Least squares fitting, criteria for goodness of fits - chi square test.