UPSC Physics Optional Syllabus:

UPSC Optional Syllabus for Physics- Paper I 

Section A

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.

2. 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.

3. 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

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.

2. 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.

3. 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.

2. 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.

3. 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.

4. 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.