Syllabus of UPSC Physics Optional Subject

Paper I:
1. Mathematical Methods of Physics
- Linear vector spaces; matrices; vector calculus; elements of complex analysis; ordinary differential equations; special functions; partial differential equations; Fourier series and Fourier transforms; Laplace transforms; elementary properties of discrete groups; groups, subgroups, and their properties; applications in physics.

2. Classical Mechanics
- Newton’s laws of motion and applications; generalized coordinates and Lagrangian and Hamiltonian formulations of mechanics; central force motion; small oscillations and normal modes; special theory of relativity; dynamics of rigid bodies.

3. Electromagnetic Theory
- Electrostatics and magnetostatics: Gauss’s law and its applications; Laplace and Poisson equations; boundary value problems; steady and time-dependent magnetic fields; Faraday’s law and induced electromotive force; Maxwell’s equations and their applications; electromagnetic waves and their propagation; Poynting vector; reflection and refraction; interference, diffraction, and polarization.

4. Quantum Mechanics I
- Wave-particle duality; Schrödinger equation; one-dimensional problems; formalism and its applications; quantum mechanics of systems with continuous variables; angular momentum; spin; addition of angular momenta; time-independent perturbation theory; elementary scattering theory.

5. Thermodynamics and Statistical Physics
- Laws of thermodynamics and their applications; kinetic theory of gases; statistical ensembles; partition function; classical and quantum statistics; ideal Bose and Fermi gases; blackbody radiation; statistics of paramagnetism.

Paper II:
6. Quantum Mechanics II
- Symmetry in quantum mechanics; time-independent perturbation theory and applications; scattering theory; relativistic quantum mechanics; introductory quantum field theory.

7. Atomic and Molecular Physics
- Structure of atoms, molecules, and solids; spectra; selection rules; X-ray and electron spectroscopy; rotational, vibrational, and electronic spectra of diatomic molecules; Franck-Condon principle; Raman effect; NMR and ESR; lasers; elementary theory and applications.

8. Nuclear and Particle Physics
- Properties of nuclei; nuclear models; nuclear reactions; fission and fusion; nuclear decay; elementary particles; fundamental forces; quark model; electromagnetic, weak, and strong interactions; particle accelerators and detectors.

9. Electronics
- Electronic devices and circuits; operational amplifiers; digital circuits; microprocessors; signal processing; communication and detection circuits; radio and television broadcasting; satellite and optical communications; medical electronics; instrumentation.

10. Solid State Physics and Materials Science
- Crystal structure; X-ray diffraction; lattice vibrations; elements of statistical mechanics; dielectric, magnetic, and superconducting properties; elements of quantum mechanics; band theory; metals, insulators, and semiconductors; electronic, magnetic, and optical properties of materials; nanomaterials and devices.

Note: The detailed syllabus for the Physics optional subject can be found on the official UPSC website or in the UPSC syllabus document.