# UPSC Physics Optional Syllabus:

## UPSC Optional Syllabus for Physics- Paper I

1. 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.
1. 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.
1. 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.
1. 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.
1. 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.
1. 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

1. 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.

1. 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.

1. 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.

1. 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.