M.Sc. DEGREE EXAMINATION, NOVEMBER 2017.
First Semester
Nano Science and Nanotechnology
BASICS OF MATHEMATICS AND QUANTUM
MECHANICS
(CBCS 2016 onwards)
Time 3 Hours Maximum 75 Marks
Part A (10 x 2 20)
Answer all questions.
1. What is meant by Curl operator?
2. What are the other operators found in operator?
3. What is the condition needed for orthogonalization?
4. State Hermite polynomial.
5. A proton moves in a cubic box 1cm on edge. How much
energy will be required to raise the proton from its lowest
energy level to a state where nx ny nz 2 .
6. State Planck's hypothesis.
7. State Superlattice.
8. What is meant by quantum confinement?
9. What is meant by negative energy states?
10. State Linear operator with example.
Sub. Code
533101
RW-881
2
Ws20
Part B x 5 25)
Answer all questions, choosing either or
11. Explain Lennard Jones potential.
Or
Write short notes on Gauss divergence theorem.
12. Discuss in detail about orthogonal properties.
Or
Explain Beta and Gamma functions.
13. Explain Harmonic oscillator.
Or
Derive the time independent Schrodinger equation.
14. Explain in detail about momentum eigen functions.
Or
Write short notes on oscillatory dynamics.
15. What are Hermitian operators? Show that the eigen
values of Hermitian operators are real.
Or
Write short notes on Dirac's equation.
RW-881
3
Ws20
Part C 10 30)
Answer any three questions.
16. Explain in detail about Diagonalization of Hermitian
matrices.
17. Give a detailed account on Hermite and Laguerre
functions.
18. Explain particle in a one dimension box in detail.
19. Explain in detail about Electron wave propagation in
devices.
20. Explain in detail about Spin angular momentum.
————————