UPESSC Assistant Professor (Physics) 2026 — Subject Code 76
Official syllabus published by the Uttar Pradesh Education Service Selection Commission for Assistant Professor (Higher Education), Physics — Subject Code 76. The written exam has 90 Physics questions and 30 General Knowledge questions.
I. Mathematical Physics and Numerical Techniques
Dimensional analysis. Vector algebra and vector calculus. Linear algebra, matrices, Cayley-Hamilton theorem, eigenvalue problems; Linear differential equations; Special functions (Hermite, Bessel, Laguerre and Legendre); Recurrence relations. Fourier series, Fourier and Laplace transforms; Elements of complex analysis: Laurent series, poles, residues and evaluation of integrals; Elementary ideas about tensors; Introductory group theory, SU(2), O(3); Elementary probability theory, random variables, binomial, Poisson and normal distributions. Numerical techniques: roots of functions, interpolation, extrapolation, integration by trapezoid and Simpson's rule, solution of first order differential equations using Runge-Kutta method; Finite difference methods.
II. Classical Mechanics
Newton's laws; Phase space dynamics, stability analysis; Central-force motion; Two-body collisions, scattering in laboratory and centre-of-mass frames; Rigid body dynamics, moment of inertia tensor, non-inertial frames and pseudoforces; Variational principle, Lagrangian and Hamiltonian formalism and equations of motion; Poisson brackets and canonical transformations; Hamilton-Jacobi theory; Symmetry, invariance and conservation laws, cyclic coordinates; Periodic motion, small oscillations and normal modes; Special theory of relativity, Lorentz transformations, relativistic kinematics and mass-energy equivalence; Twin paradox.
III. Electromagnetic Theory
Electrostatics: Gauss's law and its applications; Laplace and Poisson equations, boundary value problems; Magnetostatics: Biot-Savart law, Ampere's theorem, electromagnetic induction; Maxwell's equations in free space and linear isotropic media; boundary conditions on fields at interfaces; Scalar and vector potentials; Gauge invariance; Electromagnetic waves in free space, dielectrics and conductors; Reflection and refraction, polarization, Fresnel's law, interference, coherence and diffraction; Transmission lines and wave guides; Cavity resonator, plasma oscillation, dispersion relations in plasma; Lorentz invariance of Maxwell's equations; Dynamics of charged particles in static and uniform electromagnetic fields; Radiation from moving charges, dipoles and retarded potentials.
IV. Thermodynamics and Statistical Physics
Laws of thermodynamics and their consequences; Thermodynamic potentials, Maxwell relations; Chemical potential, phase equilibria; Phase space, macro- and microstates; Microcanonical, canonical and grand-canonical ensembles and partition functions; Free energy and connection with thermodynamic quantities; First- and second-order phase transitions; Classical and quantum statistics, ideal Fermi and Bose gases; Principle of detailed balance; Blackbody radiation and Planck's distribution law; Bose-Einstein condensation; Random walk and Brownian motion; Concept of non-equilibrium processes; Diffusion equation.
V. Quantum Mechanics
Wave-particle duality; Wave function in coordinate and momentum representations; Commutators and Heisenberg's uncertainty principle; Matrix representation; Dirac's bra and ket notation; Schrodinger equation (time-dependent and time-independent); Eigenvalue problems such as particle in a box and harmonic oscillator; Tunnelling through a barrier; Motion in a central potential; Orbital angular momentum, angular momentum algebra, spin; Addition of angular momenta; Hydrogen atom, spin-orbit coupling, fine structure; Time-independent and time-dependent perturbation theory, Fermi's Golden Rule; Selection rules; Semi-classical theory of radiation; Elementary theory of scattering, phase shifts, partial waves, Born approximation; Identical particles, Pauli's exclusion principle, spin-statistics connection; Relativistic quantum mechanics: Klein-Gordon and Dirac equations.
VI. Electronics
Semiconductor devices: diodes, junction transistors, field effect transistors, homo and heterojunctions; their structure, characteristics, frequency dependence and applications; Optoelectronic devices: solar cells, photodetectors and LEDs; Operational amplifiers and their applications; Digital techniques and applications (registers, counters, comparators and similar circuits); A/D and D/A converters; Basics of microprocessor and microcontroller; Oscillator; Amplifier; Modulation and demodulation; Switching time; High frequency devices including generators and detectors.
VII. Experimental Techniques and Data Analysis
Data interpretation and analysis; Precision and accuracy, error analysis, propagation of errors, least squares fitting, linear and nonlinear curve fitting, chi-square test; Transducers (temperature, pressure/vacuum, magnetic field, vibration, optical and particle detectors), measurement and control; Signal conditioning and recovery, impedance matching, amplification (op-amp based instrumentation and feedback), filtering and noise reduction, shielding and grounding; Fourier transforms; Lock-in detector, box-car integrator, modulation techniques.
VIII. Atomic and Molecular Physics
Quantum states of an electron in an atom; Electron spin; Stern-Gerlach experiment; Spectrum of hydrogen, helium and alkali atoms; Relativistic corrections for energy levels of hydrogen; Hyperfine structure and isotopic shift; Width of spectral lines; LS and JJ couplings; Zeeman, Paschen-Back and Stark effects; X-ray spectroscopy; Electron spin resonance, nuclear magnetic resonance, chemical shift; Rotational, vibrational and electronic spectra of diatomic molecules; Raman spectra of diatomic molecules; Franck-Condon principle and selection rules; Spontaneous and stimulated emission, Einstein A and B coefficients; Lasers, optical pumping, population inversion, rate equations; Modes of resonators and coherence length; U-V and infrared spectrometry.
IX. Condensed Matter Physics
Bravais lattices; Reciprocal lattice, diffraction and the structure factor; Bonding in solids; Elastic properties, phonons, lattice specific heat; Free electron theory and electronic specific heat; Response and relaxation phenomena; Drude model of electrical and thermal conductivity; Hall effect and thermoelectric power; Quantum Hall effect; Diamagnetism, paramagnetism and ferromagnetism; Electron motion in a periodic potential, band theory of solids; Defects and dislocations; Ordered phases of matter, translational and orientational order, liquid crystals; Conducting polymers; Quasicrystals; Superconductivity: type-I and type-II superconductors, Josephson junctions.
X. Nuclear and Particle Physics
Basic nuclear properties: size, shape and charge distribution, spin and parity; Binding energy, semi-empirical mass formula; Liquid drop model; Fission and fusion; Nature of nuclear forces, form of nucleon-nucleon potential; Charge independence and charge symmetry of nuclear forces; Isospin; Deuteron problem; Evidence of shell structure, single-particle shell model, its validity and limitations; Rotational spectra; Elementary ideas of alpha, beta and gamma decays and their selection rules; Nuclear reactions, reaction mechanisms, compound nuclei and direct reactions; Classification of fundamental forces; Elementary particles (quarks, baryons, mesons, leptons); Spin and parity assignments, isospin, strangeness; Gell-Mann-Nishijima formula; C, P and T invariance and application of symmetry arguments to particle reactions, parity non-conservation in weak interaction; Relativistic kinematics.