**FIRST SEMESTER**

Phy501: Mathematical Physics I (45L, 15T, 3CH)

Nature of the course: Theory / Full Marks: 50 / Pass Marks: 25

Course Description:

This course contains different areas of mathematics that are used extensively in the study of physics.

Objectives:

The objective of this course is to train the students to use the methods of mathematics to formulate and solve problems in physics, and make them capable to apply this knowledge in higher studies and research.

Course Contents: 1. Tensor analysis: 1.1 Law of transformations of vectors, solenoidal vectors, rotational and irrotational vectors, vortex lines 1.2 Application of Vectors 1.3 Special Orthogonal curvilinear coordinates: cylindrical, spherical and ellipsoidal. 1.4 Review of Contravarient, covariant and mixed tensors, Kronecker delta 1.5 Tensors of rank greater than two, scalars or invariants, tensor fields, symmetric and skew symmetric tensors, fundamental operations with tensors, stress tensor, 1.6 Line element and matric tensor, reciprocal tensors, associated tensors, length of a vector, angle between vectors, physical components, 1.7 Christoffel’s symbols, transformation laws of Christoffel’s symbols, geodesics, covariant derivatives, 1.8 Tensor form of gradient, divergence, curl and Laplacian. [12 hours]

2. Linear vector spaces: 2.1 Vectors in n-dimensions, linear independence, Schwartz inequality, representation of vectors and linear operators with respect to a basis, change of basis, Schmidt orthogonalization process, 2.2 Linear operators and their matrix representation with examples [4 hours]

3. Group Theory: 3.1 Introduction, 3.2 Representation of groups, 3.3 Symmetry and physics 3.4 Discrete and continuous groups 3.5 Symmetric group 3.5 Symmetric group 3.6 Orthogonal groups 3.7 Lie groups 3.8 U(1) and SU(2) groups (introduction only) [8 hours]

4. Review of Integral transforms: 4.1 Fourier transform and convolution theorem, 4.2 Laplace transform: Laplace transform of derivatives and integrals, Derivative of Laplace Transform 4.3 Use of Fourier and Laplace transform in solving partial differential equations. [5 hours]

5. Differential equations: 5.1 Review of Series solutions of Bassels’s, Legendre’s, Hermite’s, Laguerre’s differential equations, 5.2 Associated Legendre and Laguerre polynomials, orthogonality and generating functions. 5.3 Sturm-Liouville’s Theory –Self adjoint operators, Hermitian operators, completeness of eigen functions, Green’s functions-eigenfunction expansion. [10 hours]

6. Partial differential equations: 6.1 Review of Wave equations, Laplace, Poisson and diffusion equations, boundary value problems, 6.2 Green’s method of solving partial differential equations. [6 hours]

Text Books:

1. Arfken G.B. , Weber H.J. and Harris F.E – Mathematical Methods for Physicists, 7th ed., Academic Press, Amsterdam (2013)

2. Mathew, J. & Walker, R. – Mathematical Methods in Physics, Benjamin, Menlo Park, Second Edition (1970)

3. Margenu & Murphy – Mathematics for Physicist and Chemist, East West Press Pvt. Ltd., New Delhi (1964)

4. Spiegel, Murray R. – Vector Analysis (Schaum Series), McGraw Hill, London (1992)

5. Morse, P.M. & Feshbach H. – Methods of Theoretical Physics, Part I & II, McGraw Hill, New York (1953)

Reference Books:

1. Rajput B.S.– Mathematical Physics, Pragati Prakashan, India (1997)

2. Gupta B.D.– Mathematical Physics, Vikash Publishing House, India (1999)

Phy502: Classical Mechanics (45L, 15T, 3CH)

Nature of the course: Theory / Full Marks: 50 / Pass Marks: 25

Course Description:

This course contains a description and formulation of classical mechanics.

Objectives:

The objective of this course is to provide the students with knowledge of classical mechanics, and enable them to apply the knowledge for solving various problems in related topics, and also for higher studies and research.

Course Contents:

1. Constraints: 1.1 Constraints, 1.2. Generalized coordinates, generalized displacement, generalized velocity, generalized acceleration, generalized momentum, generalized force and generalized potential, 1.3. D’Alembert’s principle and Lagrange’s equations[4 hours]

2. Variational principles and Lagrange’s equations: 2.1. Calculus of variations: Geodesics, Minimum surface of revolution, The brachistochrone problem, 2.2. Hamilton’s principle and derivation of Lagrange’s equation, 2.3. Extension of Hamilton’s principle to nonholonomic systems (Method of Lagrange undetermined multipliers), 2.4. Conservation theorems and symmetry properties, 2.5. Energy function and the conservation of energy[7 hours]

3. The Central Force Problem: 3.1. Reduction to the equivalent one-body problem, 3.2 The equations of motion and first integrals, 3.3 The equivalent one-dimensional problem, and classification of orbits, 3.4 The Virial theorem, 3.5 The differential equation for the orbit, and integrable power-law potentials, 3.6 Conditions for closed orbits (Bertrand’s theorem), 3.7 The Kepler’s problem: Inverse-square law of forces, 3.8 The motion in time in the Kepler’s problem, 3.9 The Laplace-Runge-Lenz vector, 3.10 Scattering in a central force field, 3.11 Transformation of the scattering problem to laboratory coordinates[10 hours]

4. Oscillations: 4.1. Formulation of the problem, 4.2. The eigenvalue equation and the principal axis transformation, 4.3. Free vibrations of a linear triatomic molecule[3 hours]

5. The Hamilton equations of motion: 5.1. Legendre transformations and the Hamilton equations of motion, 5.2. Cyclic coordinates and conservation theorems, 5.3. Derivation of Hamilton’s equations from variational principle, 5.4. The principle of least action[4 hours]

6. Canonical transformations: 6.1. The equations of canonical transformation, 6.2. The symplectic approach to canonical transformation, 6.3 Poisson brackets and other canonical invariants, 6.4. Equations of motion, Infinitesimal canonical transformations, and Conservation theorems in the Poisson bracket formulation, 6.5 The angular momentum Poisson bracket relations, 6.6. Symmetry groups of mechanical systems[7 hours]

7. Hamilton-Jacobi theory and action-angle variables: 7.1. The Hamilton-Jacobi equation for Hamilton’s principal function, 7.2. The Hamilton-Jacobi equation for Hamilton’s characteristic function, 7.3. Separation of variables in the Hamilton-Jacobi equation, 7.4. Action-angle variables, 7.5. The Kepler problem in action-angle variables[6 hours]

8. Introduction to the Lagrangian and Hamiltonian formulations for continuous systems and fields: 8.1. The transition from a discrete to a continuous system, 8.2. The Lagrangian formulation for continuous systems, 8.4 Quantization of electromagnetic field 8.3. Hamiltonian formulation[4 hours]

Text books:

1. Herbert Goldstein, Charles Poole and John Safko, Classical Mechanics; Pearson Education (2002).

Reference books:

1. R. G. Takwale and P. S. Puranik, Introduction to Classical Mechanics, Tata McGraw-Hill (1997)

2. T. W. B. Kibble and F. H. Berkshire, Classical Mechanics, Prentice Hall (1996)

Phy503: Quantum Mechanics I (45L, 15T, 3CH)

Nature of the course: Theory / Full Marks: 50 / Pass Marks: 25

Course Description:

This course develops the formulation of quantum mechanics and its applications in various areas.

Objectives:

The objective of this course is to provide the students with adequate knowledge of non-relativistic quantum mechanics and enable them to apply the knowledge to study the atomic, molecular and other mechanical systems.

Course Contents:

1. Formulation of Quantum Theory: 1.1 Development of Quantum Theory: Copenhagen Interpretation 1.2 Review of de Broglie’s relations, wavefunctions and Schrodinger equation and Uncertainty principle.[3 hours]

2. Mathematical Tools of Quantum Mechanics: 2.1 One particle wave function space: vector space, scalar product, linear operator, closure relation, discrete and continuous bases 2.2 State space, Dirac notation: ket and bra vectors, duel space, correspondence between ket and bra, projection operator, Hermitian conjugation 2.3 Representation in state space: orthonormalization relation, closure relation, matrix representations of kets, Bras, operators, change of representations 2.4 Eigenvalue equations, observables: definition of an observable, the projectors, sets of commuting observables, complete sets of commuting observables.[10 hours]

3. Postulates of Quantum Mechanics: 3.1 Introduction 3.2 Statement of the postulates 3.3 Physical interpretation 3.4 Physical implications of the Schrodinger equation: superposition principle, conservation of probability, equation of motion for an observable, principle of first quantization, Ehrenfest theorem.[7 hours]

4. One Dimensional Barriers: 4.1 Free particle, 4.2 Concept of potential, 4.3 Potential barrier, 4.4 Ramsauer Townsend effect, 4.5 Smooth barrier, 4.6 Cold emission of electrons in a metal, 4.7 Alpha decay, 4.8 Virtual binding.[6 hours]

5. Bound States in one Dimension: 5.1 Bound states, 5.2 Parity, 5.3 Potential with finite walls, 5.4 Box normalization, 5.5 Double well model of a molecule, 5.6 Kronig-Penny model for metals, 5.7 Linear harmonic oscillator, 5.8 Creation operators, momentum representation for oscillators, 5.9 Two coupled harmonic oscillators.[8 hours]

6. Motion in Three Dimensions: 6.1 Integrals of motion, 6.2 Particle in a centrally symmetric field, 6.3 Angular solutions, 6.4 Orbital angular momentum, 6.5 Properties of spherical harmonics.[6 hours]

7. Central Potential Problems: 7.1 Two interacting particles, 7.2 Rigid rotator, 7.3 Free particle radial function, 7.4 Particle in a spherical box, 7.5 Spherical potential well of finite depth, 7.7 Isotropic harmonic oscillator, 7.8 General results for two particles bound states.[7 hours]

Text Books:

1. Agrawal, B.K. & Prakash, H. – Quantum Mechanics, Prentice Hall of India, New Delhi (1997)

2. Cohen-Tannoudji, C, Duui. B. & Laloe, F. – Quantum Mechanics, Vol. I & II, John Wiley (1977)

Reference Books:

1. Schiff, L. I.- Quantum Mechanics, 3rd ed., Tata McGraw Hill, Delhi (1968)

2. Merzbacher, E. - Quantum Mechanics, 2nd ed., John Wiley, New York (1969)

3. Messiah, A. - Quantum Mechanics, John Wiley, New York (1963)

4. Thankappan, V. K. - Quantum Mechanics, Wiley Eastern Ltd., New Delhi (1993)

Phy504: Electronics (45L, 15T, 3CH)

Nature of the course: Theory / Full Marks: 50 / Pass Marks: 25

Course Description:

This course further develops on the theory and applications of electronics.

Objectives:

The course will give an understanding of the formulation of the theory of electronics, so that the students will be able to apply the knowledge in different situations, and also in higher studies and research.

Course Contents:

Analog Electronics: Circuit Theory:

1(a) Network Transformation: 1.1 Network definition, Mesh and node circuit analysis, Principle of duality, 1.2 Reduction of complicated network, Conversions between T and π sections, 1.3 The superposition theorem, The reciprocity theorem, 1.4 Brief revision of Thevnin’s, Norton’s Theorem and The maximum power-transfer theorem, 1.5 A.C. bridge (Lattice network), Sensitivity in bridge measurements. [5 hours]

(b) Resonance: 1.6 Definition of Q, Series resonance and Band width of the series resonant circuit, 1.7 Parallel resonance circuit or anti-resonance, Condition for maximum impedance and impedance variation with frequency, 1.8 Band width of anti- resonant circuits, The general case-resistance present in both branches and anti-resonance at all frequencies.[3 hours]

Semiconductor Circuit Response and Design:

2(a) Integrated, Differential and Operational Amplifier Circuits: 2.1 Overview of CE, CC, CB and CS amplifiers, 2.2 Introduction of an ideal differential amplifier (BJT and FET), Common mode parameters, 2.3 Practical differential amplifiers, Introduction to operational amplifiers.[3 hours]

(b) Operational Amplifier Theory: 2.4 The ideal operational amplifier, 2.5 Slew rate, Offset current and voltages. [2 hours]

(c) Application of Operational Amplifiers: 2.6 Controlled voltage and current sources, 2.7 Integration, Differentiation and Wave-shaping, 2.8 Oscillators: The Barkhausen criterion, RC phase shift, Wein-bridge and Crystal, 2.9 Concept of active filters and its design, 2.10 Introduction of Clipping, Clamping and Rectifying circuits.[4 hours]

3(a) Frequency response: 3.1 Definition and basic concepts, Decibel and logarithmic plots, Series capacitance and low frequency response, 3.2 Shunt capacitance and high frequency response, Transient response, Low and high frequency response of BJT and FET amplifiers.[2 hours]

(b) Power Supply and Voltage Regulators: 3.3 Introduction, Rectifiers and different types of filters, 3.4 Voltage multipliers, 3.5 Voltage regulation: Series and shunt voltage regulators, Switching regulators, 3.7 Different types of Integrated circuit regulator (Three-terminal typeand adjusted type). [4 hours]

Digital Electronics:

4(a) Digital Circuit Analysis and Design: 4.1 Introduction, Boolean laws and theorem , 4.2 Sum of Products methods and Product of Sum methods, Truth table to Karnaugh map, Pairs, quads and octets, 4.3 Karnaugh’s simplifications.[3 hours]

(b) Data Processing Circuits: 4.4 Multiplexers, De-multiplexers, 4.5 Decoder, BCD to decimal decoders and Seven segment decoders, 4.6 Encoders, Decimal to BCD encoder, 4.7 Exclusive-OR gates, Parity generators-checkers.[3 hours]

5(a) Arithmetic Circuits : 5.1 Review of binary addition and subtraction, Unsigned binary numbers, Sign-magnitude numbers, 2’s compliment representation and its arithmetic, 5.2 Arithmetic building blocks, 5.3 The adder and subtracter, Binary multiplication and division.[3 hours]

(b) TTL Circuits: 5.5 Digital integrated circuits, 7400 Devices: Two-input TTL NAND gate, 5.6 TTL Parameters, AND-OR-INVERT gates, 5.7 Three-state TTL devices, Positive and negative logic.[3 hours]

(c) Clock and Timers: 5.9 Clock Waveforms, Review of RS Flip-Flop, 5.10 Internal structure of 555 timer, 5.11 555 Timer-Astable and Mono-stable.[3 hours]

6(a) Flip-Flops: 6.1 Review of D Flip-Flop, Edge Triggered D Flip-Flop, 6.2 Flip-Flop switching time, JK Flip-Flop, JK Master-Slave Flip-Flip, 6.3 Schmitt trigger.[3 hours]

(b) Shift Registers: 6.4 Types of registers (Serial in - Serial out, Serial in - Parallel out, Parallel in - Serial out, Parallel in - Parallel out), 6.5 Ring counters.[2 hours]

(c) Counters: 6.6 Asynchronous counters, Decoding gates, 6.7 Synchronous counters, Shift Counters.[2 hours]

Text Books:

1. Ryder, J.D. – Network, Lines and Fields, Prentice Hall of India (1955)

2. Bogart, T.F. – Electronics Devices and Circuits, Universal Book Stall, New Delhi (1995).

3. Malvino, A.P and Leach, D.P. – Digital Principles and Application, Tata McGraw Hill Publishing Company Ltd., New Delhi (1991).

Reference Books:

1. Malvino A.P. – Electronic Principles, Tata McGraw Hill Publishing Company, New Delhi (1984).

2. Boylestad, R.L. and Nashelsky , L. – Electronic Devices and Circuit Theory, 8th edition, Prentic Hall of India Private Ltd., New Delhi (2004)

3. Floyd, T.L. – Digital Fundamentals, 8th edition, Pearson Education, Inc. (2005)

4. Jain R.P. – Modern Digital Electronics, Tata McGraw Hill Publishing Company Ltd., New Delhi (1984).

Phy505: Physics Practical I (Compulsory) (Lab180, T45, 3CH)

Nature of the course: Practical / Full Marks: 50 / Pass Marks: 25

Course Description:

Practical course consists of four sections: (a) General Experiments, (b) Optical Experiments, (c) Nuclear Experiments and (d) Electronics Experiments. In the M.Sc. physics first semester, students have to perform 16-20 experiments in 180 working hours in order to fulfill 3 CH. Students are required to perform 3 hours laboratory work each day. In addition, there will be 45 hours computation class in order to learn the method of data analysis using suitable software. They have to write a laboratory report on each experiment they perform and get them duly checked and signed by the concerned teacher. They should write their reports in a separate sheet, and to keep them neat and properly filed. Students are required to perform at least 15 experiments from the list (given below).

Course Objectives:

1. To provide students with skill and knowledge in the experimental methods.

2. To make them able to apply knowledge to practical applications.

3. To make them capable of presenting their results/conclusions in a logical order.

Course Contents:

1. To study the Fresnel biprism for the determination of the wavelength of a given monochromatic light and thickness of mica sheet.

2. To study Lloyd’s mirror for the determination of wavelength of Hg light.

3. To study the formation of fringe pattern by wedge shape.

4. To study the variation of refractive index with concentration of sugar solutions using a hollow prism.

5. To design and study the series and parallel LCR circuits for finding the quality factor of the elements.

6. To study the absorption of β-particle by material to estimate the end-point energy of the β-particle.

7. To study the absorption of γ-ray by the material of lead to determine its linear absorption coefficient, μ.

8. To study the level of natural background radiation at the laboratory in the given condition

9. To construct regulated power supply unit.

10. To construct CE amplifier for the determination of the voltage gain of the amplifier.

11. To construct CC amplifier for estimating input and output impedance.

12. Use Zener diode to construct a variable regulated power supply.

13. To construct astable multivibratorusing 555 timer and study its performance.

14. To construct monostable multivibratorusing 555 timer and study its function.

15. To construct and to study the characteristics of RS flip-flop and J-K flip-flop.

16. To construct a voltage multipliers (doubler and tripler) and study its characteristics.

17. To construct and study the working of NOT, AND, OR gates using diodes and transistors. Also calculate the power loss in transistors in each case wherever it is applicable.

18. Solve the given equation using K-map and construct the circuit with verification.

**SECOND SEMESTER**

Phy551: Mathematical Physics II (45L, 15T, 3CH)

Nature of the course: Theory / Full Marks: 50 / Pass Marks: 25

Course Description:

This course contains different areas of mathematics that are used extensively in the study of physics.

Objectives:

The objective of this course is to train the students to use the methods of mathematics to formulate and solve problems in physics, and make them capable to apply this knowledge in higher studies and research.

Course Contents:

1. Complex variable: 1.1 Functions of a complex variable, single and multi valued functions, Riemann sheets 1.2 Analytic functions and Cauchy – Riemann conditions, 1.3 Analytic continuation 1.4 Cauchy integral theorem and formula, 1.5 Taylor and Laurent expansions of functions of a complex variable, 1.6 Residue theorem and applications, 1.7 Conformal transformations 1.8 Dispersion relation.[15 hours]

2. Numerical analysis (use of computer is optional): 2.1 Interpolation and extrapolation: approximation of given data by a polynomial, interpolation and extrapolation of data, 2.2 Solution of equation: polynomial equation, determination of roots, 2.3 Numerical integration: trapezoidal, Simpson and Romberg method, 2.4 Matrices: eigen values and eogen vectors, inverse of square matrix by Gauss-Jordan elimination method, 2.5 Differential equation: solution of differential equation by Runge-Kutta method.[14 hours]

3. Statistics: 3.1 Review of Data handling: histogram, mean, mode, median and standard deviation, moments, skewness, Kurtosis, 3.2 Distribution functions: bionomial, normal and Poisson distributions, 3.3 Curve fitting: least square fit for straight lines and curves, 3.4 Chi-square tests: observed and theoretical frequencies, significance tests, goodness of fit, central limit theorem, 3.5 Error analysis.[10 hours]

4. Differential Geometry: 4.1 Introduction - Application of differential geometry in physics 4.2 differentiable manifolds 4.3 Tangent and co-tangent space 4.4 Vector fields.[6 hours]

Text Books:

1. Arfken G.B. , Weber H.J. and Harris F.E – Mathematical Methods for Physicists, 7th ed., Academic Press, Amsterdam (2013)

2. Copson, E.T. – An Introduction to the Theory of Functions of Complex Variable, Oxford Clarendon Press (1935)

3. Mathew, J. & Walker, R. – Mathematical Methods in Physics, Benjamin Menlo Park, Second Edition (1970)

4. Margenu & Murphy – Mathematics for Physicist and Chemist, East, West Press Pvt. Ltd., New Delhi (1964)

5. Scarborough J.B. – Numerical Analysis, John Hopkins Press, USA (1962)

6. Press, M. et al. – Numerical Recipe in C, Cambridge University Press, or, Foundation Book, India (1998)

7. Morse, P.M. & Feshbach H. – Methods of Theoretical Physics, Part I & II, McGraw Hill, New York (1953)

8. Spiegel Murray R. – Theory and Problems of Statistics (Schaum Series), McGraw Hill, London (1992)

9. Isham C. J.- Modern Differential Geometry for Physicists, World Scientific Lecture Notes in Physics – Vol 61, 2nd ed. World Scientific, Singapore (2001)

Reference Books:

1. Rajput B.S.– Mathematical Physics, Pragati Prakashan, India (1997)

2. Gupta B.D.– Mathematical Physics, Vikash Publishing House, India (1994)

Phy552: Statistical Mechanics (45L, 15T, 3CH)

Nature of the course: Theory / Full Marks: 50 / Pass Marks: 25

Course Description:

This course contains a description and formulation of statistical mechanics.

Objectives:

The objective of this course is to provide the students with knowledge of statistical mechanics, and enable them to apply the knowledge for solving various problems in related topics, and also for higher studies and research.

Course Contents:

1. Classical statistical mechanics: 1.1 Review of Thermodynamics 1.2 The statistical basis of thermodynamics 1.3 Review of classical mechanics – Hamiltonian equation of motion 1.4 Macroscopic and microscopic states, 1.5 Phase space, 1.6 Liouville’s theorem 1.7 Postulate of statistical mechanics 1.8 Microcanonical ensemble 1.9 Derivation of thermodynamic properties 1.10 Classical ideal gas 1.12 Gibb’s paradox 1.13 Classical harmonic oscillators in Microcanonical Ensemble 1.13 Canonical ensemble 1.14 Partition function 1.15 Energy fluctuation in canonical ensemble 1.16 Grand Canonical ensemble Energy and density fluctuations in grand canonical ensemble 1.17 Classical ideal gas in canonical and grand canonical ensemble 1.18 Classical harmonic oscillators in Canonical Ensemble 1.19 Equivalence of various ensembles, 1.20 Thermodyanmics of magnetic systems: negative temperature 1.21 Generalized equipartition theorem – theorem of equipartition of energy and virial theorem 1.22 Virial Theorem -equation of state for classical interacting particles. [18 hours]

2. Quantum statistical mechanics: 2.1 Postulates of quantum statistical mechanics 2.2 Density matrix and its properties 2.3 Ensembles in quantum statistical mechanics – microcanonical, canonical, and grand canonical ensembles 2.4 Partition functions with examples including (I) an electron in magnetic field (II) a free particle in a box (III) a linear harmonic oscillator 2.5 Third law of thermodynamics 2.6 Symmetric and antisymmetric wave functions 2.7 The ideal gases: Microcanonical ensemble 2.8 The ideal gases: grandcanonical ensemble 2.9 Grand partition function 2.10 Occupation number 2.11 Partition functions for diatomic molecule.[12 hours]

3. Application of Ideal Bose and Fermi syatems: 3.1 Thermodynamical behavior of ideal Bose gas, 3.2 Photons –Black body radiation and Planck’s law of radiation, 3.3 Thermodynamics of weakly degenerate Bose gas, 3.4 Thermodynamics of strongly degenerate Bose gas – Bose-Einstein condensation and liquid helium4 3.5 Phonons in solids, specific heat of solids 3.6 Thermodynamical behavior of ideal Fermi gas – weakly and strongly degenerate Fermi gas, 3.7 Free electron in metals, 3.8 Statistical equilibrium of white dwarf and neutron stars.[10 hours]

4. Phase Transitions: 4.1 Condensation of van der Waals gas 4.2 A dynamical model of phase transitions, 4.3 Ising model.[5 hours]

Text books:

1. Kerson Huang - Statistical Mechanics; John Wiley (1987)

Reference books:

1. R. K. Pathria - Statistical Mechanics, Butter Worth Heinemann, New Delhi, India (1996)

2. A. Mc Quarrie - Statistical Mechanics, Harper and Row, New York (1973)

3. R. Reif - Fundamental of Statistical and Thermal Physics, McGraw-Hill Book Company, New York (1965)

4. L.D. Landau & E.M. Lifshitz - Statistical Physics, Vol. 5, Pergamon Press (1969)

Phy553: Solid State Physics (45L, 15T, 3CH)

Nature of the course: Theory / Full Marks: 50 / Pass Marks: 25

Course Description:

This course develops the basic formulation of solid state physics and its applications in various areas.

Objectives:

The objective of this course is to provide the students with adequate knowledge of solid state physics and enable them to apply the knowledge to study the atomic, molecular and other mechanical systems.

Course Contents:

1. Crystal Structure: 1.1 Translation symmetry - periodic array of atoms 1.2 Simple lattice, 1.3 Index systems for crystal planes 1.4 Review of Simple crystal structures: NaCl, CsCl, hexagonal closed packed, diamond and cubic zinc sulfide structure 1.5 Reciprocal lattice, Brillouin zone, 1.6 Crystal diffraction, 1.7 Structure factor, 1.8 Crystal binding: a) Van der waal’s crystals, b) ionic crystals, c) Metals, d) Covalent crystals, e) Hydrogen bonded crystals, 1.7 Elastic constants and their determination.[9 hours]

2. Lattice Vibration: 2.1 Vibration of crystals with monoatomic basis, 2.2 Vibration of crystals with two atoms per primitive basis, 2.3 Quantization of elastic waves, 2.4 Phonon momentum, 2.5 Inelastic scattering by phonon, 2.6 Thermal properties of solid: density of states in one, two and three dimensions, 2.7 Phonon heat capacity: Review of Debye and Einstein’s model, 2.8 Thermal Conductivity 2.9 Anharmonic crystal interaction: Thermal expansion.[7 hours]

3. Electrons in bands: 3.1 Review of Nearly free electron model, Bloch theorem, Kronig-Penny model, 3.2 Wave equation of electron in periodic potential, 3.3 Number of orbitals in a band, 3.4 Calculation of energy Bands: Tight binding approximation, Wigner Seitz method, cohesive energy, pseudopotential methods 3.5 Fermi surface: Construction of Fermi surfaces – nearly free electrons, Electron orbits, hole orbits and open orbits 3.6 Experimental methods in Fermi surface studies: quantization of orbits in a magnetic field, de Haas-van Alphen effect, Fermi surface of copper and gold.[13 hours]

4. Semiconductor: 4.1 Band diagram of semiconductor, 4.2 Intrinsic carrier concentration, 4.3 Impurity conductivity: thermal ionization of donors and acceptors.[3 hours]

5. Dielectric properties: 5.1 Dielectric constant and polarizability, 5.2 Electronic, ionic and orientational polarizabilities, 5.3 Complex dielectric constant 5.4 Dielectric losses and relaxation time.[4 hours]

6. Magnetism: 6.1 Diamagnetism and paramagnetism, 6.2 Quantum theory of diamagnetism of mononuclear systems, 6.3 Quantum theory of paramagnetism, Hund rules 6.4 Magnetic ordering, 6.5 Ferrommagnetic order: Curie point and exchange integral, Temperature dependence of the saturation magnetization, ferromagnetic domains, Bloch wall, Saturation Magnetization at Absolute zero, 6.6 Magnons, thermal excitation of magnons, 6.6 Ferrimagnetic order: Curie temperature and susceptibility 6.7 Antiferrimagnet, susceptibility below Neel temperature.[9 hours]

Text books:

1. Kittel C. – Introduction to Solid State Physics, (7th Ed.) John Wiley & Sons Ltd, India (2004)

References:

1. Ibach H. and Luth H. – Solid State Physics, Narosa Publishing House, New Delhi (1991)

2. Ashcroft NW and Mermin ND - Solid State Physics, Holt Rinehart and Winston. New York (1976).

3. Elliot R. J. & Gibson A. F. – An Introduction to Solid state Physics and its Application, Macmillan (1974).

4. Hall H. E. – Solid State Physics, Wiley (1974)

5. Walter A. Harrison – Solid State Theory, Curier Dover Publication (1970).

6. Dekker A. J. – Solid State Physics, Printice Hall (1965).

7. Ziman J.M. – Principles of Theory of Solids, Cambridge University Press (1979)

Phy504: Electrodynamics I (45L, 15T, 3CH)

Nature of the course: Theory / Full Marks: 50 / Pass Marks: 25

Course Description:

This course further develops on the theory and applications of electrodynamics.

Objectives:

The course will give an understanding of the formulation of the theory of electrodynamics, so that the students will be able to apply the knowledge in different situations, and also in higher studies and research.

Course Contents:

1. Introduction to Electrostatics: 1.1 Review of the Electrostatic Field and Electrostatic Potential 1.2 Poisson and Laplace equations 1.3 Green’s theorem 1.4 Uniqueness of the solution with Dirichlet or Neumann boundary conditions 1.5 Formal solution of electrostatic boundary-value problem with Green Function.[4 hours]

2. Boundary Value Problems in Electrostatics: 2.1 Methods of image 2.2 Point charge in the presence of a (a) grounded conducting sphere (b) Charged insulated conducting sphere 2.3 Conducting sphere in a uniform electric field by method of image 2.4 Green function for the sphere and general solution for the potential 2.5 Conducting sphere with hemisphere at different potentials 2.6 Laplace equation in spherical coordinates and boundary value problems with azimuthal symmetry 2.7 Associated Legendre functions and the spherical harmonics Ylm, Use of addition theorem for spherical harmonics 2.8 Expansion of Green function in spherical coordinates.[10 hours]

3. Multipoles, Electrostatics of Macroscopic Media, Dielectrics: 3.1 Multipole expansion 3.2 Multipole expansion of the energy of a charge distribution in an external field 3.3 Elementary treatment of electrostatics with ponderable media 3.4 Boundary value problem with dielectrics 3.5 Electrostatic energy in dielectric media.[6 hours]

4. Magnetostatics: 4.1 Review of Magnetostatics (Biot and Savart law, Ampere’s law, Vector potential) 4.2 Magnetic fields of a localized current distribution, magnetic moment 4.3 Force and torque on the energy of a localized current distribution in an external magnetic induction, 4.4 Macroscopic equations, Boundary conditions on B and H, 4.5 Method of solving boundary value problems in magnetostatics 4.6 Uniformly magnetized sphere 4.7 Magnetized sphere in an external field, permanent magnets 4.8 Faraday’s law of induction 4.9 Energy in the magnetic field.[8 hours]

5. Maxwell’s Equations: 5.1 Maxwell’s equations 5.2 Vector and scalar potentials 5.3 Gauge Transformations, Lorenz Gauge, Coulomb Gauge 5.4 Green functions for the wave equation 5.5 Poynting’s theorem and conservation of energy and momentum for a system of charged particles and electromagnetic fields 5.6. Poynting's Theorem in Linear Dispersive Media with Losses.[7 hours]

6. Electromagnetic Waves and Wave Propagation: 6.1 Plane waves in nonconducting medium 6.2 Linear and circular polarization; Stokes Parameters 6.3 Reflection and Refraction of electromagnetic waves at a plane interface between dielectrics 6.4 Polarization by Reflection and Total Internal Reflection 6.5 Frequency Dispersion Characteristics of Dielectrics, Conductors, and Plasmas 6.6 Simplified Model of Propagation in the Ionosphere and Magnetosphere. [7 hours]

7. Waveguides, Resonant Cavities: 7.1 Fields at the surface of and within a conductor 7.2 Cylindrical cavities and waveguides 7.3 Waveguides 7.4 Modes in a rectangular waveguide.[3 hours]

Text Books:

1. Jackson, J.D. – Classical Electrodynamics (3rd Ed.), John Wiley & Sons Asia Pvt Ltd. (1999).

Reference Books:

1. Panofsky, W.K.H. and Philips - Classical Electricity and Magnetism, Addison–Wesley Publishing Company, Inc. USA or Indian Book Company New Delhi (1970).

2. Born, Max and Wolf E. – Principle of Optics, Elsevier Holland (1980).

3. Reitz, J. R. and Milford F.J. – Foundation of Electromagnetic Theory, Addison Wesley Publishing Company (1975).

4. Miah M.A. and Wazed – Fundamentals of Electromagnetic (3rd Ed.) Tata McGraw Hill Publishing Company Ltd. New Delhi (1982).

5. Griffiths David J.- Introduction to Electrodynamics (4th Ed.), Addison-Wesley (2013).

Phy555: Physics Practical II (Compulsory) (Lab180, T45, 3CH)

Nature of the course: Practical / Full Marks: 50 / Pass Marks: 25

Course Description:

Practical course consists of four sections: (a) General Experiments, (b) Optical Experiments, (c) Nuclear Experiments and (d) Electronics Experiments. In addition, there is a computation laboratory in order to learn computational/numerical technique. In the M.Sc. physics second semester, students have to perform 15 experiments in 180 working hours in order to fulfill 3 CH. Students are required to perform 3 hours laboratory work each day. In addition, there will be 45 hours computation classes in order to learn the method of data analysis using suitable software. They have to write a laboratory report on each experiment they perform and get them duly checked and signed by the concerned teacher. They should write their reports in a separate sheet, and to keep them neat and properly filed. Students are required to perform at least 14 experiments from the list (given below).

Course Objectives:

1. To provide students with skill and knowledge in the experimental methods.

2. To make them able to apply knowledge to practical applications.

3. To make them capable of presenting their results/conclusions in a logical order.

Course Contents:

1. To determine the half life of the given radioactive source. (nuclear lab)

2. To study the phenomenon of Back-Scattering using a thin radioactive source. (nuclear lab)

3. To study the phenomenon of hysteresis loss of the material and to determine the hysteresis loss of the material over a cycle. (general lab)

4. To study the Lissajous pattern for the determination of the frequency of a given unknown source. (general lab)

5. To study the current–voltage characteristics of a photocell and hence use photoelectric method to determine the value of Plank’s constant. (optical lab)

6. To study the specific heat capacity of the materials using Calorimetric method. (general lab)

7. To study the temperature dependence of resistance of a given semiconductor. (general lab)

8. To study differential amplifier and estimate it’s CMRR.(electronics lab)

9. To construct and to study the Exclusive-OR and Exclusive-NOR gates by using universal gates. (electronics lab)

10. To study operational amplifier for its input-output waveform and use it as an integrator and differentiator. (electronics lab)

11. To study the working of half adder and full adder. (electronics lab)

12. To construct and study the Wien-bridge. (electronics lab)

13. To construct D/A converter and to study its working. (electronics lab)

14. To study the characteristic of a FET and construct it to work as an amplifier. (electronics lab)

15. Solve given numerical problem using computation. (computation lab)

**THIRD SEMESTER**

(will be added later)

**FOURTH SEMESTER**

(will be added later)**NOTE:**

1. Mid-Term and Final-Term exams will be held on schedule. Students should notify HoD with supplement documents if they unable to attend due to health and accidental problem. These exams can be rescheduled by the allocated faculties if HoD recommends.

2. Final Practical Examination will be held on schedule. This exam will be compulsory (will not be rescheduled).

© 2014 Institute of Science and Technology, Research Team-Central Department of Physics.

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