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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.

GET UPSC CSE SYLLABUS HERE: https://www.naukripakad.com/upsc-cse-syllabus/

CHECK MORE OPTIONAL SUBJECT SYLLABUS AT https://www.naukripakad.com/upsc-cse-optional-subjects-and-syllabus/

### SYLLABUS FOR PAPER I

SECTION A:

1. 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
1. 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
1. 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

1. 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
1. 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
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

### SYLLABUS FOR PAPER II

1. 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
1. 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
1. 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
• Conservation laws
• Field quanta of electroweak and strong interactions
• Physics of neutrinos
• Elementary ideas about unification of forces
1. 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 Author
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