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Course Code
L T
3 1
Quantum Mechanics for Nanotechnology
Co-requisite:
Prerequisite:
Data Book /
Codes/Standards
XXX
YYY, ZZZ, WWW
Course Category
Course designed by
Approval
P
PROFESSIONAL CORE
Department of Physics and Nanotechnology
-- Academic Council Meeting -- , 2016
P
0
C
4
Clark’s Table, IS : 456-2000
Quantum Mechanics for
Nanotechnology
To provide a working knowledge of the foundations, techniques, and key results of quantum mechanics
for solving problems in nanotechnology.
INSTRUCTIONAL OBJECTIVES
STUDENT
OUTCOMES
At the end of the course, student will be able to
1. Explain the origin of old and new Quantum Mechanics
a
2. Explain the bound and scattering state and can solve the numerical
a
c
3. Correlate quantum physics behind applications - Nano Dimension
a
4. Solve the many body problems using various assumptions
a
5. Start the core subjects of Nanotechnology based on Quantum Phenomena
a
PURPOSE
Session
Description of Topic
UNIT I: BASIC FORMULATION & BOUND STATE PROBLEMS
Contact
hours
9
C-DI-O
IOs Reference
1.
Old quantum mechanics, Statistical interpretation and normalization
of wave function
2
C
1
1,2,3
2.
Schrödinger’s time dependent and time independent wave equations
2
C,D
1
1,2,3
3.
Stationary states, Heisenberg uncertainty principle, Ehrenfest theorem
2
C,D,I 1
1,2,3
4.
Infinite square well in one and three dimensions, Delta function
potential, Finite square well.
UNIT II: SCATTERING STATES & QUANTUM TUNNELING
3
C,D,I 1
1,2,3
9
5.
Scattering states, reflection and transmission of particles
2
C,D,I 2
1,2,3
6.
Delta function potential well and barrier Step potential
2
C,D
2
1,2,3
7.
Rectangular potential barrier, Tunnel effect, Double delta function
potential barriers
3
D,I
2,3
1,2,3
8.
Resonant tunneling
2
C
2,3
1,2,3,4
UNIT III: DISCRETE EIGENVALUE PROBLEMS
9
Energy Eigen functions and Eigen values coordinates precession.
3
C,D.I 3
1,2,3,4
10. Spherical Harmonic oscillator in one dimension, momentum, Eigen
values
2
C,D
1,2,3,4
Schrödinger equation in spherical coordinates, Angular equation,
11. Radial equation, Infinite Spherical well, Ground state properties of
hydrogen atom
2
C,D,I 3
1,2,3,4,5
12. Angular momentum, Eigenvalues, Spin 1/2
2
C,D,I 3,4
1,2,3,4,5
9.
UNIT IV: APPROXIMATION METHODS
9
3
13. Time independent perturbation theory for non-degenerate and
degenerate energy levels
14. Variation method, Time-dependent perturbation theory for two-level
systems
15. Sinusoidal perturbations, Incoherent perturbation, Transition rate,
Adiabatic and Sudden approximations (Elementary concepts).
UNIT V: IDENTICAL PARTICLES AND SCATTERING
THEORY
16. Two particle system’s Schrödinger equation, Transformation to center
of mass frame from laboratory frame
3
C,D
4,5
1,2,3,4,5
3
C,D
4,5
1,2,3,4,5
3
C,D
4,5
1,2,3,4,5
3
C,D
4,5
1,2,3,4,5
17. Symmetrization of wave function, Bosons and Fermions, Exchange
forces, Solids, Free electron gas
3
C,D
4,5
1,2,3,4,5
Band structure, Quantum Scattering theory, Differential and total
18. cross sections, Green’s functions, Born approximation, Application to
spherically symmetric potentials.
3
C,D,I 4,5
1,2,3,4,5
Total contact hours
9
45
LEARNING RESOURCES
Sl.
TEXT BOOKS
No.
1.
David J. Griffiths, “Introduction to Quantum Mechanics”, Second Edition, Pearson, 2009.
2.
Ajoy Ghatak and S. Lokanathan, “Quantum Mechanics”, Fifth Edition, Macmillan, 2009.
REFERENCE BOOKS/OTHER READING MATERIAL
3.
Bransden B.H., and Joachain C.J., “Quantum Mechanics”, Second Edition, Pearson, 2007.
4.
YoavPeleg, ReuvenPnini, ElyahuZaarur, and Eugene Hecht, “Schaum’s Outline of Quantum Mechanics”,
Second Edition, Tata McGraw Hill, 2010.
5.
Mathews P.M. and Venkatesan K.,“Quantum Mechanics”,Second Edition, Tata McGraw Hill, 2010.
Course nature
Assessment Method (Weightage 100%)
Assessment tool Cycle test I
In-semester
Weightage
10%
Theory
Cycle test II
15%
Cycle Test III
Surprise Test
Quiz
15%
5%
5%
End semester examination Weightage :
Total
50%
50%