**Quantum Mechanics**

Schrodinger wave equation: One dimensional problem, particle in a box, tunnelling through a potential barrier, linear harmonic oscillator, K-P model; Particle in a central potendial: Hydrogen atom; WKB approximation method; Perturbation theory for degenerate & non-degenerate cases: First and second order perturbation, applications-Zeeman effect & Stark effect; Time dependent perturbation theory; Variation method: Application to He atom & van der Waals interaction between two hydrogen atoms; Pauli spin materices; Dirac equation: System of identical particles; many electron system-Hatree & Hatree-Fock approximation.

**Advanced Quantum Mechanics**

Radiation Theory: Quantization of Schrodinger field, scattering in Born approximation, quantization of classical radiation field, Emission probability of photon, angular distribution of radiation, intensities of Lyman lines, Compton effect and Bremstrahlung.

Path Integral: Approach to quantum mechanics, the principle of least action, quantum mechanical amplitude, path integrals, the path integral as function, the Schrodinger equation for a particle ina field of potential V(x), the Schrodinger equation for the keruel.

**Physics of Deformed Solids**

Theory of matter transport by defect mechanism: Random walk theory and correlation effects in metals and alloys for impurity and self-diffusion: Theory of ionic transport process, impurity defect association, long range interactions, dielectric loss due to defect dipoles, Internal friction, Radiation damage in metals and semiconductors, colour centres: mechanism of production by various methods, Optical and magnetic properties and models of different colour centre; Theoretical calculation of atomic displacement and energies in defect lattices and amorphous solids, stress-strain and dislocations; Elasticity theory of strees field around edge and screw dislocations, Dislocation interactions and reactions effects on mechanical properties.

**X-ray Crystallography**

X-ray: production and properties of X-rays, continuous and discrete X-ray spectra, Reciprocal lattice, structure factor and its application, X-ray diffraction from a crystal, X-ray techniques: Weissangerg and precession methods, identification of crystal structure from powder photograph and diffraction traces, Laue photograph for single crystal, geometrical and physical factors affecting X-ray intensities, analysis of amorphous solids and fibre textured crystal.

**Low Temperature Physics and Vacuum Techniques**

Production of low temperature; Thermodynamics of liquefaction; Joule-Thompson liquefiers; Cryogenic system design: Cryostat design, heat transfer, temperature control, adiabatic demagnetization; Different types of pumps: rotary, diffusion and ion pumps, pumping speeds, conductance & molecular flow; Vacuum gauges: Mclead gauge, thermal conducitivity ionization gauges; Cryogenic thermometry: gas & vapour pressure thermometers, resistance, semiconductor and diode capacitance thermometers, thermocouples, magnetic thermometry.

**Physics of Semiconductors and Superconductors**

Intrinsic, extrinsic, and degnerate semiconductors; Density of states in a magnetic field; Transport properties of semiconductors; thermo-electric effect, thermomagnetic effect, Piezo-electric resistance, high frequency conductivity; contact phenomena in semiconductors: metal-semiconductor contacts, p-n junction, etc. Optical and photoelectrical phenomena in semiconductors: light absorption by free charge, charge carriers, lattices, and electrons in a localized states, photoresistive effect, Dember effect, photovoltaic effect, Faraday effect, etc.

Phenomena of superconductivity: Pippard?s non-local electrodynamics, thermodynamics of superconducting phase transition; Ginzburg-Landau theory; Type-I and type-II superconductors, Cooper pairs; BCS theory; Hubbard model, RVB theory, Ceramic superconductors: synthesis, composition, structures; Thermal and transport properties: Normal state transport properties, specific heat; role of phonon, interplay between magnetism and superconductivity: Possible mechanism other than electron-phonon interaction for superconductivity.

**Solid State Physics**

Lattice dynamics of one, two & three dimensional lattices, specific heat, elastic constants, phonon dispersion relations, localized modes; Dielectric and optical properties of insulators: a.c. conductivity dielectric constant, dielectric losses; Transport theory: Free electron theory of solids: density of states, Fermi sphere, Electrons in a periodic potential; Band theory of solids: Nearly free electron theory, tight binding approximation, Brillouin zones, effective mass of electrons and holes.

**Polymer Physics**

Introduction to macromolecular physics: The chemical structure of polymers, Internal rotations, Configurations, and Conformations, Flexibility of macromolecules, Morphology of polymers; Modern Concept of polymer structure: Physical methods of investigatiing polymer structure such as XRD, UV-VIS, IR, SEM, DTA/TGA, DSC, etc., the structure of crystalline polymers; The physical states of polymers: The rubbery state, Elasticity, etc.; The glassy state, Glass transition temperature, etc., Viscosity of polymers; Advanced polymeric materials: Plasma polymerization, Properties and application of plasma-polymerized organic thin films; Polymer blends and composites: Compounding and mixing of polymer, Their properties of application; Electrical properties of polymers: Basic theory of the dielectric properties of polymers, Dielectric properties of structure of cyrstalline and amorphous polymers.

**Optical Crystallography**

The morphology of crystals, the optical properties of crystals, the polarizing microscopy, general concept of indicatrix, isotropic and uni-axial indicatrix, orthoscopic and conscopic observation of interference effects, orthoscopic and conscopic examination of crystals. Optical examination of uni-axial and bi-axial crystals, determination of retardation and birefringence, extinction angles, absorption and pleochroism, determination of optical crystallographic properties.

**Magnetism-I**

Classification of magnetic materials, Quantum theory of paramagnetism, Pauli paramagnetism, Properties of magnetically ordered solids; Weiss theory of ferromagnetism, interpretation of exchange interaction in solids, ferromagnetic domains; Technical magnetization, intrinsic magnetization of alloys; Theory of antiferromagnetic and ferrimagnetic ordering; Ferrimagnetic oxides and compounds.

**Magnetism-II**

Magnetic anisotropy: pair model and one ion model of magnetic anisotropy, Phenomenology of magnetostriction, volume amgnetostricition and form effect; Law of approach of saturation, Structure of domain Wall, Technological applications of magnetic materials.

**Thermodynamics of Solids**

Properties at O.K, Gruneisen relation, Heat capacities of crystals, specific heat arising from disorder. Rate of approach of equality, Variation of compressibility with temperature, relation between thermal expansion and change of compressibility with pressure. Thermodynamics of phase transformation and chemical reactions. Thermodynamic properties of alloy system: Factors determining the crystal structure; The Hume-Rothery rule, the size of ions; Equilibrium between phases of variable composition, Free energy of binary systems; Thermodynamics of surface and interfaces, Thermodynamics of defects in solids.

**Experimental Techniques in Solid State Physics**

Measurement of D.C. conductivity, dielectric constant and dielectric loss as a function of temperature and frequency, Magnetization measurement methods (Faraday, VSM and SQUID) magnetic anisotropy and magnetostriction measurements, magnetic domain observation, optical spectroscopy (UV-VIS, IR, etc.), Electron microscopy; Differential thermal analysis (DTA) and thermogravimetric analysis (TGA), Deposition and Growth of thin films by vacuum evaporation Production of low temperature. Single crystal growth and orientation. Magnetic and non-magnetic annealing; Electron spin resonance (ESR), Ferromagnetic resonance (FMR) and nuclear magnetic resonance (NMR).

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Referencia Bibliografica:

www.cuet.ac.bd/downloads/MPhil%20Syllabus.doc