LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – PHYSICS
SIXTH SEMESTER – APRIL 2012
PH 6609/PH 6605/6003/6600 – QUANTUM MECHANICS & RELATIVITY
Date : 16-04-2012 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
SECTION – A
Answer ALL the questions: (10 × 2 = 20 Marks)
- Mention the important properties of de Broglie waves.
- What are the important applications of an electron microscope?
- Give the physical significance of the wave function.
- What do you mean by tunneling through a potential barrier?
- What is Hermitian operator?
- Show that [Lx, Ly] = i ħ Lz.
- What will be the speed of a photon in one reference frame if it moves with a speed c in another frame of reference?
- Calculate the rest mass energy of an electron in eV.
- State Mach’s principle.
- State the principle of equivalence.
SECTION – B
Answer any FOUR questions: (4 × 7.5 = 30 Marks)
- (a) Distinguish between optical microscope and electron microscope. (5)
(b) Calculate de-Broglie wavelength associated with a proton moving with (1/30)c
(h= 6.62 × 10-34Js and m = 1.67×10-27kg). (2.5)
- (a) Write down Schrödinger equation and eigen values for a linear harmonic
(b) Discuss zero point energy. (3.5)
- (a) What do you mean by eigen functions and eigen values? (1.5+1.5)
(b) Prove that every eigen value of Hermitian operator is real. (4.5)
- On the basis of Lorentz transformations discuss (i) length contraction and (ii) time dilation. (4+3.5)
- (a) What do you mean by inertial mass and gravitational mass? (1.5+1.5)
(b) Discuss the Red shift of spectral lines in a gravitation field. (4.5)
SECTION – C
Answer any FOUR questions: (4× 12.5 = 50 Marks)
- (a) Describe, with neat diagrams, the experiment of Davisson and Germer on the
diffraction of electrons to establish the wave nature of matter. (10)
(b) If the uncertainty in the location of a particle is equal to its de Broglie wavelength,
What is the uncertainty in its velocity? (2.5)
- Solve the Schrödinger equation for a particle moving in one dimensional potential well
of finite depth to find eigen functions and eigen values.
- Solve the radial part of Schrödinger equation for the hydrogen atom to obtain eigen
values of energy.
- Describe the Michelson-Morley experiment and discuss the various interpretations for
the negative result of the experiment. (10+2.5)
- Discuss the motion of a planet in the gravitational field of the sun and explain the
advance of the perihelion of Mercury. (8+4.5)
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