Mathematical Physics
Unit-I
Orthogonal Curvilinear coordinate system, scale factors, expression for gradient, divergence and curl and their applications to Cartesian, cylindrical and spherical polar coordinate systems, Coordinate transformation and Jacobian, Transformation of covariant, contravariant and mixed tensor, Addition, Multiplication and contraction of tensors, Quotient law, pseudo tensor, Metric tensor, transformation of Tensors.
Unit-II
Dirac-Delta Function and its properties, Fourier series, computation of Fourier coefficients, applications to simple periodic functions like square wave, sawtooth wave and rectifier out put, Postulates of special theory of relativity and observational evidence, Lorentz transformation and rotation in space time, time like and space like vectors, length contraction, time dilation, worldline, mass-energy relation, energy-momentum relation.
Unit-III
Four vector formulation, energy-momentum four vectors, relativistic equation of motion, Orthogonality of four forces and four velocities, transformation of four wave vector, longitudinal and transverse Doppler’s effect, Transformation between laboratory and center of mass systems, four momentum conservation, Kinematics of decay products of an unstable particles and reaction thresholds, pair production, inelastic collision of two particles, Compton effect. Electromagnetic field tensor, transformation of four potentials, four currents, electric and magnetic field between two inertial frames of reference, Lorentz force, equation of continuity, conservation of charge, tensor description of Maxwell’s equations.
Unit-IV
The second order linear differential equation with variable coefficient and singular points, series solution method and its application in the Bessel’s, Hermite’s, Legendre’s and Laguerre’s differential equations, Basic properties like orthogonality, recurrence relations, graphical representation and generating function of Bessel, Hermite, Legendre Laguerre and Associated Legendre functions.
Unit –V
Technique of separation of variables and its application to following boundary value problems: (i) Laplace equation in three dimension Cartesian Coordinate system-line charge between two earthed parallel conducting plates, (ii) wave equation in spherical polar coordinates - the vibration of circular membrane, (iii) Diffusion equation in two dimensional Cartesian coordinate system-heat conduction in thin rectangular plate, (iv) Laplace equation in spherical coordinate system
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Solid State Physics
Unit-I
Crystal Binding and Crystal Structure: Crystal bonding, ionic bond, binding energy of ionic crystal, determination of the repulsive exponent, covalent bonding, metallic bonding, molecular or Vander Waal’s bonding, hydrogen bonding, Space lattice and Crystal structure, reciprocal lattice, Bravis lattice, Miller indices, Spacing of planes in Crystal Lattice, Atomic Packing, Simple cubic structure, Face centered cubic structure, Hexagonal closed packed structure, Pervoskite structure, X-ray diffraction and Bragg’s law, Laue pattern.
Unit-II
Thermal Properties of Solids, Concepts of Thermal Energy and Phonons, Internal Energy and Specific Heat, The Various theories of Lattice specific Heat of Solids, The Einstein Model, Vibrational Modes of Continuous Medium, Debye Model, Electronic Contribution of the internal Energy to the Specific Heat of Metals, Thermal Conductivity of the Lattice.
Unit-III
Band Theory of Solids, Formation of bands, Periodic Potential of a solid, Wave function in a Periodic Lattice and Bloch Theorem, Number of States in the Band, Kronig Penny model, Velocity of the Bloch electrons and Dynamical effective mass, Momentum, Crystal Momentum and Physical Origin of the Effective Mass, Negative Effective Mass and Holes, The distinction between metals, insulators and intrinsic semiconductors.
Unit-IV
Electrical Conductivity, Drude-Lorentz Theory of Electrical Conductivity, Boltzmann Transport Equation, Sommerfeild Theory of Electrical Conductivity, Mathiessen’s Rule, Thermal Conductivity and Widemann-Franz’sLaw, The Hall Effect. Superconductivity, Introduction, Meisnner’s effect, The Isotope Effect and Electron-Phonon Interaction, The Effect of the Superconductivity Transition on properties, Special Features of Superconducting Materials, London’s equation, Flux Quantization, Qualitative discussion of BCS Theory of Superconductivity, Cooper Pairs, Applications of Superconductors, Josephson Junction.
Unit-V
Magnetic Properties, Origin of Atomic Magnetism, Dynamics of Classical Dipole in Magnetic field, Magnetic Susceptibility, Diamagnetism, Paramagnetism, Paramagnetism of Ionic Crystal, Ferromagnetism, Temperature Dependance of saturation of Spontaneous Magnetization, The Paramagnetic Region, The nature of ferromagnetism, Nature and Origin of Weiss Molecular Field, Heisenberg’s Exchange Interaction, Quantum Theory of Ferromagnetism, Relation between Jo (Exchange Integral) and I (Weiss Constant), Ferromagnetism Domain.
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Basic Instrumentation Techniques
UNIT-I
Basic of Measurement: Instruments accuracy, precision, sensitivity, resolution range etc. Errors in measurements and loading effects. Multimeter: Principles of measurement of dc voltage and dc current, ac voltage, ac current and resistance. Specifications of a multimeter and their significance. Digital Instruments: Principle and working of digital meters. Comparison of analog & digital instruments. Characteristics of a digital meter. Working principles of digital voltmeter. Digital Multimeter: Block diagram and working of a digital multimeter.
UNIT- II
Electronic Voltmeter: Advantage over conventional multimeter for voltage measurement with respect to input impedance and sensitivity. Principles of voltage, measurement (block diagram only). Specifications of an electronic Voltmeter/ Multimeter and their significance. AC millivoltmeter: Type of AC millivoltmeters: Amplifier- rectifier, and rectifier- amplifier. Block diagram ac millivoltmeter, specifications and their significance.
UNIT- III
Cathode Ray Oscilloscope: Block diagram of basic CRO. Construction of CRT, Electron gun, electrostatic focusing and acceleration (Explanation only– no mathematical treatment), brief discussion on screen phosphor, visual persistence & chemical composition. Time base operation, synchronization. Front panel controls. Specifications of a CRO and their significance. Use of CRO for the measurement of voltage (dc and ac frequency, time period. Special features of dual trace, introduction to digital oscilloscope, probes. Digital storage Oscilloscope: Block diagram and principle of working.
UNIT- IV
Signal Generators and Analysis Instruments: Digital techniques and applications (registers, counters, comparators and similar circuits). A/D and D/A converters. Microprocessor and microcontroller basics.
UNIT- V
Data interpretation and analysis. Precision and accuracy. Error analysis, propagation of errors. Least squares fitting, High frequency devices (including generators and detectors). Block diagram, explanation and specifications of low frequency signal generators. pulse generator, and function generator. Brief idea for testing, specifications. Distortion factor meter, wave analysis.
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List of Experiments
Note- One experiment must be performed in the semester examination. Marks distribution will be as: Experiment - 30, Practical record – 10, Viva Voce – 10.
1. Determine the value of Plank’s constant using photocell.
2. Determine the value of Plank’s constant using solar cell.
3. Work function of Tungsten, Richardson’s equation.
4. Determine hall voltage, mobility, carrier concentration and hall coefficient in a given semiconductor.
5. Determine the magnetic susceptibility of a paramagnetic salt by Quinck’s method.
6. Determine hysterisis loss using CRO.
7. Study the dynamics of a lattice using electrical analogue.
8. Study the characteristics of a G.M counter and verify the inverse square law.
9. Study of β- absorption in aluminium foil using G.M counter.
10. Study of variation of modulus of rigidity of a given specimen as a function of temperature.
11. Any other experiments of the equivalent standard can be set.