1. The Kronig-Penney model.
2. N-particle linear chain model.
3. Scalar potental in the cylindrical magnet.
4. Parallel-plate capacitor in two dimensions.
5. Heat flow in a metal bar.
6. Semiclassical quantization of molecular vibrations: Bohr-Sommerfeld quantization for bound states of the Lennard-Jones Potential
7. Hartree-Fock solutions of small atomic systems in the filling approximation.
8. Ground state of many electron system using density functional theory (DFT).
9. Calculation of energy bands in crystals.

1.Introduction: Moore’s law and technology development. International Technology Roadmap for Semiconductors (ITRS); Technology and material challenges limiting Moore’s law.

2.Contacts: Fabrication of Junction, Metal-semiconductor contacts, Schottky barrier. Contact resistance: 2-probe and 4-probe measurements; Kelvin and van der Pau structures; pn junctions: carrier transport. Equilibrium conditions, Steady state conditions, Transients and AC conditions.

1. Physics at low temperature: production and measurement at ultra-low temperatures. Hecryostats, adiabatic and nuclear demagnetization, dilution refrigerators, Pomeranchuk effect, physical properties of materials at low temperatures. Electrical transport, thermal,mechanical, optical and magnetic properties. Bose-Einstein condensates, BEC in ultra-coldatomic gases. Superfluidity: superfluid 4He, classical and quantum fluids, macroscopic wavefunction, superfluid properties of He-II, flow quantization and vortices, the momentum distribution, quasi-particle excitations. Second sound.

1. X-rays: X-ray diffraction: estimation of crystallographic parameters, X-ray fluorescence: elemental identification of given samples (9 hours)
2. Optical absorption spectra of materials, estimation of (direct / indirect) band-gap (6 hours)
3. Hall effect: estimation of carrier concentration, Hall voltage and carrier mobility (9 hours).
4. Zeeman effect (6 hours)
5. Temperature-dependent current measurements: estimation of activation energy (6 hours)
6. Raman spectrometer: stokes and anti-stokes lines (6 hours)
7. Rydberg constant: hydrogen spectrum – differ

1.Fundamental concepts: Kets, bras, and operators. Base kets and matrix representations. Measurements, observables, and the uncertainty relations. Change of basis. Position eigenkets and position measurements. Wave functions in position and momentum space. Momentum operator in the position basis. Gaussian wave packets.

2.Quantum dynamics: Time evolution and the Schrӧdinger equation. The Schrӧdinger versus the Heisenberg picture. Schrӧdinger wave equation. Particle-in-a-box problem, Simple harmonic oscillator.

1.Crystal structure

Periodic arrays of atoms: basis and the crystal structure, primitive lattice. Fundamental types of lattices: 2 and 3 dimensional lattice types, Bravais lattice. Index system for crystal planes. Simple crystal structures with examples. Reciprocal lattice: diffraction of waves by crystals, Bragg’s law. Reciprocal lattice vectors, Brillouin zones.

2. Band structure:

1. Revision of thermodynamics: isolated, closed and open systems, reversible and irreversible processes. Zeroth and first laws: heat, internal energy and enthalpy, Joule- Thompson coefficient. Second law: entropy. Gibb’s free energy, Third law: statements (Nernst, Planck and Lewis).

1)Revision of electromagnetic theory: Fields and potentials (Coulomb’s law, Gauss’ theorem, Poisson’s and Laplace’s   equations, Ohm’s law, Kirchhoff’s law, Ampere’s law, Gauss’s magnetic field law, Lorentz field     equation, Faraday’s   law, Maxwell’s modification of Ampere’s law), fields in vacuum and in matter. Maxwell’s equations.

2)Field interaction with matter: dipole moments and polarization. Field and potential due to electric dipoles and   multipole fields. Equation of continuity, relaxation time of charges in dielectrics and metals.