**UPSC Optional Syllabus for Physics- Paper I **

Section A |

**Classical Mechanics:**

**1.1. Particle dynamics:**

- Centre of mass and laboratory coordinates, conservation of linear and angular momentum.
- The rocket equation.
- Rutherford scattering, Galilean transformation, inertial and non-inertial frames, rotating frames, centrifugal and Coriolis forces, Foucault pendulum.

**1.2. System of particles:**

- Constraints, degrees of freedom, generalised coordinates and momenta.
- Lagrange’s equation and applications to linear harmonic oscillator, simple pendulum and central force problems.
- Cyclic coordinates, Hamiltonian Lagrange’s equation from Hamilton’s principle.

**1.3. Rigid body dynamics:**

- Eulerian angles, inertia tensor, principal moments of inertia.
- Euler’s equation of motion of a rigid body, force-free motion of a rigid body.
- Gyroscope.

**Special Relativity, Waves & Geometrical Optics:**

**2.1. Special Relativity:**

- Michelson-Morley experiment and its implications.
- Lorentz transformations- length contraction, time dilation, addition of velocities, aberration and Doppler effect, mass-energy relation, simple applications to a decay process.
- Minkowski diagram, four dimensional momentum vector.
- Covariance of equations of physics.

**2.2.Waves:**

- Simple harmonic motion, damped oscillation, forced oscillation and resonance.
- Beats.
- Stationary waves in a string.
- Pulses and wave packets.
- Phase and group velocities.
- Reflection and Refraction from Huygens’ principle.

**2.3. Geometrical Optics:**

- Laws of reflection and refraction from Fermat’s principle.
- Matrix method in paraxial optic-thin lens formula, nodal planes, system of two thin lenses, chromatic and spherical aberrations.

**Physical Optics:**

**3.1. Interference:**

- Interference of light-Young’s experiment, Newton’s rings, interference by thin films, Michelson interferometer.
- Multiple beam interference and Fabry-Perot interferometer.
- Holography and simple applications.
**3.2. Diffraction:**

- Fraunhofer diffraction-single slit, double slit, diffraction grating, resolving power.
- Fresnel diffraction: – half-period zones and zones plates.
- Fresnel integrals.
- Application of Cornu’s spiral to the analysis of diffraction at a straight edge and by a long narrow slit.
- Diffraction by a circular aperture and the Airy pattern.

**3.3. Polarisation and Modern Optics: **

- Production and detection of linearly and circularly polarised light.
- Double refraction, quarter wave plate.
- Optical activity.
- Principles of fibre optics attenuation; pulse dispersion in step index and parabolic index fibres; material dispersion, single mode fibres.
- Lasers- Einstein A and B coefficients.
- Ruby and He-Ne lasers. Characteristics of laser light-spatial and temporal coherence. Focussing of laser beams.
- Three-level scheme for laser operation.

Section B |

**Quantum Mechanics I:**

- Wave-particle dualitiy.
- Schroedinger equation and expectation values.
- Uncertainty principle.
- Solutions of the one-dimensional Schroedinger equation free particle (Gaussian wave-packet), particle in a box, particle in a finite well, linear harmonic oscillator. Reflection and transmission by a potential step and by a rectangular barrier.
- Use of WKB formula for the life-time calculation in the alpha-decay problem.

**Quantum Mechanics II & Atomic Physics:**

**2.1. Quantum Mechanics II: **

- Particle in a three dimensional box, density of states, free electron theory of metals.
- The angular meomentum problem.
- The hydrogen atom.
- The spin half problem and properties of Pauli spin matrices.

**2.2. Atomic Physics: **

- Stern-Gerlack experiment, electron spin, fine structure of hydrogen atom.
- L-S coupling, J-J coupling.
- Spectroscopic notation of atomic states. Zeeman effect.
- Frank-Condon principle and applications.

**Molecular Physics:**

- Elementary theory of rotational, vibrational and electronic spectra of diatomic molecules.
- Raman effect and molecular structure.
- Laser Raman spectroscopy Importance of neutral hydrogen atom, molecular hydrogen and molecular hydrogen ion in astronomy Fluorescence and Phosphorescence. Elementary theory and applications of NMR.
- Elementary ideas about Lamb shift and its significance

**UPSC Optional Syllabus for Physics- Paper II**

**Quantum Mechanics:**

Wave-particle dualitiy; Schroedinger equation and expectation values; Uncertainty principle; Solutions of the one-dimensional Schroedinger equation for a free particle (Gaussian wave-packet), particle in a box, particle in a finite well, linear harmonic oscillator; Reflection and transmission by a step potential and by a rectangular barrier; Particle in a three dimensional box, density of states, free electron theory of metals; Angular momentum; Hydrogen atom; Spin half particles, properties of Pauli spin matrices.

**Atomic and Molecular Physics:**

Stern-Gerlach experiment, electron spin, fine structure of hydrogen atom; L-S coupling, J-J coupling; Spectroscopic notation of atomic states; Zeeman effect; FrankCondon principle and applications; Elementary theory of rotational, vibratonal and electronic spectra of diatomic molecules; Raman effect and molecular structure; Laser Raman spectroscopy; Importance of neutral hydrogen atom, molecular hydrogen and molecular hydrogen ion in astronomy; Fluorescence and Phosphorescence; Elementary theory and applications of NMR and EPR; Elementary ideas about Lamb shift and its significance.

**Nuclear and Particle Physics:**

Basic nuclear properties-size, binding energy, angular momentum, parity, magnetic moment; Semi-empirical mass formula and appl icat ions, mass parabolas; Ground state of deuteron, magnetic moment and non-central forces; Meson theory of nuclear forces; Salient features of nuclear forces;Shell model of the nucleus – successes and limitations; Violation of parity in beta decay; Gamma decay and internal conversion; Elementary ideas about Mossbauer spectroscopy; Q-value of nuclear reactions; Nuclear fission and fusion, energy production in stars; Nuclear reactors.

Classification of elementary particles and their interactions ; Conservation laws ; Quark structure of hadrons; Field quanta of electroweak and strong interactions; Elementary ideas about unification of forces; Physics of neutrinos.

**Solid State Physics, Devices and Electronics:**

Crystalline and amorphous structure of matter; Different crystal systems, space groups; Methods of determination of crystal structure; X-ray diffraction, scanning and transmission electron microscopies; Band theory of solids – conductors, insulators and semiconductors; Thermal properties of solids, specific heat, Debye theory; Magnetism: dia, para and ferromagnetism; Elements of superconductivity, Meissner effect, Josephson junctions and applications; Elementary ideas about high temperature superconductivity.

Intrinsic and extrinsic semiconductors; pn-p and n-p-n transistors; Amplifiers and oscillators; Op-amps; FET, JFET and MOSFET; Digital electronics-Boolean identities, De Morgan’s laws, logic gates and truth tables; Simple logic circuits; Thermistors, solar cells; Fundamentals of microprocessors and digital computers.