LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.Sc. DEGREE EXAMINATION – PHYSICS
SUPPLEMENTARY EXAMINATION – JUNE 2008
PH 3900 - QUANTUM MECHANICS
Date : 27-06-08
Time : 9:00 - 12:00
Dept. No.
Max. : 100 Marks
SECTION – A
Answer all the questions.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
10 x 2 = 20 Marks
What are matter waves?
Give the probability interpretation of the wave function.
Mention any two properties of a linear operator.
x 
If A   1  , find A , A A and A A
 x2 
If [ x,px] = iħ , evaluate [x,px2]
If a, a† are the lowering and raising operators of quantum harmonic oscillator, evaluate [a†a,a],
given that [a, a†] =1
State Heisenberg’s uncertainty principle.
Express mathematically the orthonormal properties of eigenvectors with continuous
eigenvalues.
Represent a finite square potential barrier mathematically and diagrammatically.
What is meant by degeneracy?
SECTION – B
Answer any four questions.
11.
12.
13.
14.
15.
4 x 7.5 = 30 Marks
Obtain the Schrodinger time independent equation from time dependent equation.
Show that if any two operators A and B commute, they are simultaneously measurable.
Prove Heisenberg’s uncertainty principle.
Obtain the eigenvalues of a linear harmonic oscillator.
Using separation of variable, separate the θ and φ part of the eigenvalue equation of L2
operator.
SECTION – C
Answer any four questions.
4 x 12.5 = 50 Marks
16.
(a) State Planck’s hypothesis.
(b)What is photoelectric effect? Give Einstein’s explanation of photoelectric effect.
17.
Show that for non-degenerate case
(a) the eigenvalues of a Hermitian operator are real.
(b) the eigenkets of a Hermitian operator are orthogonal.
18.
(a) Mention five different properties of Dirac-delta function.
(b) Show how unitary transformation can bring about a change of basis.
19.
Explain the phenomenon of quantum mechanical tunnelling through a
square potential
barrier.
20.
Obtain the eigenvalues by solving the radial part of the Schroedinger equation for the
hydrogen atom.
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