Scheme m. Sc. Physics Nano–Science & Technology



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Semester II



NT 1.2.1 QUANTUM MECHANICS
Maximum Marks: External 60 Time Allowed: 3 Hours

Internal 20 Total Teaching hours: 50



Total 80 Pass Marks: 35%
Out of 80 Marks, internal assessment (based on two mid-semester tests/ internal examinations, written assignment/project work etc. and attendance) carries 20 marks, and the final examination at the end of the semester carries 60 marks.
Instruction for the Paper Setter: The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from respective section of the syllabus. Section C will have 10 short answer type questions, which will cover the entire syllabus uniformly. Each question of sections A and B carries 10 marks. Section C will carry 20 marks.
Instruction for the candidates: The candidates are required to attempt two questions each from sections A and B, and the entire section C. Each question of sections A and B carries 10 marks and section C carries 20 marks.
Use of scientific calculators is allowed.

SECTION A

Wave Mechanics: Review of wave mechanical principles. Time independent Schrodinger equation in one, two and three dimensions. Eigen values and Eigen functions. Bound states. Discrete eigen values. Orthogonality of eigen functions. Completeness of eigen functions. Box and function normalization. Expectation values of observables. Uncertainty principle.

Particle in a one dimensional box with finite walls. Two dimensional square with infinite walls. Three dimensional rectangular box with infinite walls and three dimensional square well potential. Isotropic Harmonic oscillator. Degeneracy.


Matrix Mechanics: Postulates of quantum mechanics. Hilbert space. Matrix representation of wave functions and operators. Dirac bra and Ket notations. Change of basis. Harmonic oscillator problem in matrix mechanics creation, destruction and number operators. Orbital angular momentum operators in their polar form . Commutation relation. Matrix representation of orbital angular momentum operators. Eigen values and eigen vectors of L2, Lz spin angular momenta and Pauli spin matrices. Addition of angular momenta. Clebsch-Gordan coefficients. C.G. coefficients of .

SECTION B
Approximation methods for bound states: Stationary non degenerate perturbation theory, Ist and second order correction to energy levels, Ist order correction to wave functions, Anharmonic oscillator,
Degenerate perturbation theory. Normal Zeeman effect and stark effect of the first excited state of hydrogen.
The Rayleigh Ritz variational method for ground and excited states. Ground state of He atom perturbation and variational approaches and their comparison.
Van der Waal's interaction. Perturbation and vibrational calculations.
One dimensional WKB approximation. Asymptotic behaviour of solutions. Linear turning points. Connection formula and their application to bound state and barrier penetration.
Collision Thoery: Two particle scattering problem. Differential and total scattering cross-section. Lab and CM system of coordinates. Scattering of a particle by a central field. Partial wave analysis. Phase shifts S & P wave scattering. Ramsauer Townsend effect. Resonant scattering. Scattering for a three dimensional square well and rigid sphere. Integral equation for scattering problem. Born approximation. Validity of Born approximation. Screened Coulomb potential.

Text Books:

  1. Quantum Mechanics: L.I. Schiff (Int. Student Ed.), Tata Mc Graw-Hill , New Delhi.

  2. Quantum Mechanics: J.L. Powell and B. Craseman, Narosa Publishing House, New Delhi.

  3. Quantum Mechanics; Mathew & Venkatesan, Tata Mc Graw Hill, New Delhi.


NT 1.2.2 DIGITAL ELECTRONICS
Maximum Marks: External 60 Time Allowed: 3 Hours

Internal 20 Total Teaching hours: 50

Total 80 Pass Marks: 35%
Out of 80 Marks, internal assessment (based on two mid-semester tests/ internal examinations, written assignment/project work etc. and attendance) carries 20 marks, and the final examination at the end of the semester carries 60 marks.
Instruction for the Paper Setter: The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from respective section of the syllabus. Section C will have 10 short answer type questions, which will cover the entire syllabus uniformly. Each question of sections A and B carries 10 marks. Section C will carry 20 marks.
Instruction for the candidates: The candidates are required to attempt two questions each from sections A and B, and the entire section C. Each question of sections A and B carries 10 marks and section C carries 20 marks.
Use of scientific calculators is allowed.

SECTION A

Binary, octal and hexadecimal number systems, Inter-conversion of binary to decimal, Decimal to binary, Octal to binary, hexadecimal to binary numbers, Binary arithmetic.


Binary codes, the 8421 code, Gray code and ASCII codes.
Boolean algebra and logic gates-Boolean variables, NOT, AND, OR, NAND, NOR and exclusive OR operation, Boolean identities and laws of Boolean algebra, DeMorgan's theorem, Combinational and sequential logic systems, Minterm and Maxterm and mapping.

Switching properties of semiconductor devices, Diode, BJT and FET as DC and AC switches, Combinational logic circuits using digital ICs.


Sequential and combinational systems. RS, JK, D and T flip-flops, Counters, Synchronous counters, Serial, parallel and mixed counters

SECTION B

Shift registers and ring counters, Universal shift registers

Semiconductors memories, Memory organization and operation, Expanding memory size, Classification and characteristics of memories, Sequential memory, Read only memory, Read and write memory.
Variable register network, Binary ladder, D/A convertor, D/A accuracy and resolution, A/D converters, Simultaneous conversion, Counter method, A/D converters
Characteristics of digital ICs, Classification of logic families, Digital IC packages.
Text Books:


  1. Digital Principles: A.P. Malvino and D.P. Leach, Tata McGraw-Hill Pub. Co. Ltd. New Delhi.

  2. Modern Digital Electronics: R.P. Jain, Tata McGraw-Hill Pub. Co. Ltd., New Delhi.


Reference Books:

  1. Microelectronics: Jacob Millman and Arvin Grabel (3rd Ed.), McGraw Hill Book Co., New Delhi.

  2. Digital Systems: Principle and Applications: Ronald J. Tocci (Vth Ed.), PHI, New Delhi.

  3. An Introduction to Digital electronics: M.Singh, Kalyani Publishers, New Delhi.


NT 1.2.3 FUNDAMENTALS TO NANOTECHNOLOGY
Maximum Marks: External 60 Time Allowed: 3 Hours

Internal 20 Total Teaching hours: 50



Total 80 Pass Marks: 35%
Out of 80 Marks, internal assessment (based on two mid-semester tests/ internal examinations, written assignment/project work etc. and attendance) carries 20 marks, and the final examination at the end of the semester carries 60 marks.
Instruction for the Paper Setter: The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from respective section of the syllabus. Section C will have 10 short answer type questions, which will cover the entire syllabus uniformly. Each question of sections A and B carries 10 marks. Section C will carry 20 marks.
Instruction for the candidates: The candidates are required to attempt two questions each from sections A and B, and the entire section C. Each question of sections A and B carries 10 marks and section C carries 20 marks.
Use of scientific calculators is allowed.
SECTION A
Definition of Nanotechnology, Nanoscience & nature, Need of nanotechnology, Size dependence of properties, Quantum confinement effect, Effective mass approximation, Weak confinement regime, Intermediate confinement regime, Strong confinement regime, Empirical pseudopotential method, Tight binding model, Statistical effects of spatial confinement.
Properties of Isolated nanoparticles & nanocrystalline powders: Structural & phase transformations, Crystal lattice constant, Phonon spectrum & heat capacity, magnetic properties, optical properties, catalytic properties.
Effect of grain size & interfaces on the properties of bulk nanomaterials: Mechanical properties, Thermal properties, electric properties, magnetic properties.

Metal Nan clusters: Magic numbers, Theoretical modeling of nanoparticles, Geometric structure, Electronic structure, Reactivity, Fluctuations, Magnetic clusters.
Rare gas & Molecular Clusters: Inert gas clusters, Superfluid clusters, Molecular clusters, Self assembly.Organic compounds and polymers, Biological nanostructures.
Bulk Nanostructure Materials: Solid disordered nanostructures, Nanostructured multi-layers, Metal nanocluster composite glasses, porous silicon.
Nanostructure Crystals: Natural Crystals, Arrays of nanoparticles in zeolites, crystal of metal particles, Nanoparticle lattice in colloidal suspensions, Photonic crystals.

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