For a UPSC CSE aspirant, the optional subject is also an important subject. In the UPSC mains exam, optional marks have two papers, Paper 1 and Paper 2. Each paper is of 250 marks which makes a total of 500 marks. The UPSC optional subject list contains 48 subjects in total, one of which is Physics.

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**SYLLABUS FOR PAPER I**

**SECTION A:**

**Classical Mechanics:**

**1.1. Particle dynamics:**

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

**1.2. System of particles:**

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

**1.3. Rigid body dynamics:**

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

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

**2.1. Special Relativity:**

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

**2.2.Waves:**

- Simple harmonic motion, damped oscillation, forced oscillation, and resonance
- Stationary waves in a string
- Beats
- Phase and group velocities
- Pulses and wave packets
- 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, a system of two thin lenses, spherical and chromatic aberrations

**Physical Optics:**

**3.1. Interference:**

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

**3.2. Diffraction: **

- Fresnel diffraction: – half-period zones and zones plates
- Fraunhofer diffraction-single slit, double slit, diffraction grating, resolving power
- 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, a quarter-wave plate
- Principles of fibre optics attenuation
- Optical activity
- Pulse dispersion in step-index and parabolic index fibres
- Lasers- Einstein A and B coefficients
- Material dispersion, single-mode fibres
- Ruby and He-Ne lasers
- Characteristics of laser light-spatial and temporal coherence
- Three-level scheme for laser operation
- Focussing of laser beams

**Section B**

**Quantum Mechanics I:**

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

**Quantum Mechanics II & Atomic Physics:**

**2.1. Quantum Mechanics II: **

- Particle in a three-dimensional box, the density of states, free electron theory of metals
- The hydrogen atom
- Properties of Pauli spin matrices
- Problems on angular momentum, spin half problem

**2.2. Atomic Physics: **

- Stern-Gerlack experiment, electron spin, the fine structure of hydrogen atom
- Spectroscopic notation of atomic states
- L-S coupling, J-J coupling
- 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

**SYLLABUS FOR PAPER II**

**Quantum Mechanics:**

- Wave-particle duality
- Uncertainty principle
- Schroedinger equation and expectation values
- 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, the density of states, free electron theory of metals
- Hydrogen atom
- Properties of Pauli spin matrices
- Angular momentum
- Spin half particles

**Atomic and Molecular Physics:**

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

**Nuclear and Particle Physics:**

- Basic nuclear properties-size, binding energy, angular momentum, parity, magnetic moment
- The ground state of deuteron, magnetic moment, and non-central forces
- Semi-empirical mass formula and applications, mass parabolas
- Meson theory of nuclear forces
- Salient features of nuclear forces
- Shell model of the nucleus – successes, and limitations
- Gamma decay and internal conversion
- Violation of parity in beta decay
- 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
- Quark structure of hadrons
- Conservation laws
- Field quanta of electroweak and strong interactions
- Physics of neutrinos
- Elementary ideas about unification of forces

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

- The crystalline and amorphous structure of matter
- Methods of determination of crystal structure
- Different crystal systems, space groups
- X-ray diffraction, scanning, and transmission electron microscope
- Thermal properties of solids, specific heat, Debye theory
- Band theory of solids – conductors, insulators, and semiconductors
- Magnetism: dia, para, and ferromagnetism
- Elements of superconductivity, Meissner effect, Josephson junctions, and applications
- Elementary ideas about high-temperature superconductivity
- p-n-p and n-p-n transistors
- Intrinsic and extrinsic semiconductors
- 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
- Fundamentals of microprocessors and digital computers
- Thermistors, solar cells