Bharathiar University 2000 M.Sc Physics Classical Mechanics,Statistical Mechanics and reality - Question Paper
Degree
13, (a) State and explain the law of equipartition of energy.
Or
(b) Explain the relation of thermodymmieal variable to the partition fractions.
14, (a) Briefly compare the three statistics.
. _ Or
Cb) Give an accotmt of Bose-liasteia coadessatioa.
15, (a) Explain the Riemann tensor and Mcei tensor,
' Or
(b) Give m account of the covariant Lagrangian
formxilatlon.
SECTION C (5 x 8 s 40 marks) .
'
Answer ALL the questions, choosing either (a) or Cb).
16, (a) Derive the equations of canonical transformations.
ibi Biscaa ILe lias.uioaic oscillator problem by tLe Hamilton-4acobi method.
1?, (a) Derive the Eulers equations of .motion.
(b) Discus"- the three type of motion of a symmetrical top.
18. (a) Give a detailed account of Doppler broadening of the spectral lines.
(b) Obtain the expressions for the vibration a! r?.cl rotational partition functions.
19. (a) Apply B.E. statistics to explain law of blackbody radiation,
(b) Arrive at an expression for the paramagnetic susceptibility of a free electron gas: ,
20. (a) Discuss the relatmstic generalization of Newtons laws.
. Or
fh) Explain the covariant Hamiltonian formulation.
5 172
(For the candidates admitted from 1999 and oawaxds) M.Bc. DEGREE KMffilOM NOVEMBER 2000,
First Semester HI Branch HI Fhymes
CLASSICAL, STAHSTICA'MBCHANICS AND
HLTmff-Paper III
Time : Three hoisrs ' Maximum : 100 marks
SECTION (10 x 2 s 20 marks)
Anrw&r ALL the questions.
? '
Choose the correct anrrrer.
1. M foactioiis whose* Poisson Bracket with the Hamiltonian vanish will be
(&) the same
(fc>) infinite
vC/ xexo
(<0 - constats of motion.
2d
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(e) ultraviolet region (d) visiHe region. |
Symmetric linear molecules ctahavs
(a) only odd values of J
(b) only even values
(c values of J
neither odd or even values.
The condensation temperature is also called as
4.
(a) transition temperature
(bj-'pritical temperature
'(c) degeneracy temperature
(d) Fermic temperature.
*
Two Lorentz transformations carried out in
session are equivalent to
(a) an orthogonal transformation
Cb) one Lorentz transformation
(c) a Galilean transformation '
id) uona of the above.
Answer the following questions in ONE or TWO ' -
sent*,aces: f. V nSfi fB,_ W\
6. Distinguish Lagrange and Poisson bracketsr-a? vj J
7. ' What elders .angles? ' , j
i;
8. Explain partition functions. j
9. State Paulis exclusion principle. -* tAmji be. rn.
t principle, tauntA te.
pcAI-icJi, *li\ i|v*; - <
metric tensor? ' -
**. --*"
10. What do you mean by metric tensor?
SECTION B (5 x 4 = 20 marks) Answer ALL questions, choosing either (a) or (b)
11. (a) If #,fJ be the Poisson bracket of $ or v ,
Mffl
show that I#*?]52 at '
Or
(b) Explain aetion-angle vambies. Brrng out the significance of their use.
3 172
SECTION D (2 x 10 = 20 marks)
Answer ALL the questions, choosing either (a) or (b),
21 (a) Defee Poisson brackets. Obtai the equation . of motim is Poisson bracket notation.
Or
' (b) Discuss in detail the free vibrations of a triatomic molecule and obtain the expression for normal frequencies.
22. {a) Employing M.B. distribution obtain an expression for the energy of a harmonic oscillator. Write a note on the specific beat of perfect gases.
' Or
(b) Outline the theory of electrons m metals considering the degenerate case.
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| Earning: Approval pending. |
