Bharathiar University 2001 M.Sc Physics Quantum Mechanics -I - Question Paper
Degree
9, How andare related?
10, Define r4 and matrices, SECTION B (5x4 = 20 marks)
11,. (a) What does |aj{o{ signify? Explain,
(b) Using Diracs notation, show that the Trace
I
12. (a) Discuss iterative technique used in variation
method.
Or '
*
(b) Explain why Stark effect is not observable for the ground state of hydrogen atom.
13. (a) What is rsear.t tv Harmonic perturbation?
r
(b) Explain the reason for the potential scattering.
14. (a) Show that </, </, j= 0.
Or
(b) If
r
C - h yF(7'"+T)~~m (m +1) mi C ~ $+m) (/-m+l)
obtain the matrix element (vCilAJ %}, where L. Wm * C+ rra+l and _ijrw =C. v-1*
15, (a) Show that faxeyia,|~2s< where cect ,
~ are Dirac's matrices, * .
Or
(b) State the properties of r-matrlces (any two). SECTION (5x8 = 40 marks)
16, (a) Discass th* salient features of interaction picture. Obtain the characteristic equation.
i.b) Considering the behavioar of an electron in a periodic potential (Kroxug-Fenny model), obtain the condition for the solutions of the wave function to exist, if the wave nature is as shown here.
*
>x
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1$
r*
(For th candidates admitted from 1999 awards) M.Sc, DEGREE EXAMINATION, NOVEMBER 2001. Second Semester , Fiiyeiics QUANTUM MECHANICS -1 Time : Three hours Maximum ; 100 marks
Answer ALL questions.
Choose the correct answer,
1, An operator a is said to be a unit operator, if
(a) (A i a | A) = 0
U) (AjorjA) = 1
Id) a|A) = {A|.
h(0 1
a
2
CO
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2. The energy- correct;;:. for the states a = 2, wl h,. are affected by electric field are
(a) 3%e, *
(b) -3s0e,3%
(c) Both are 3a0eE only . -
M) 3aueS, ~3ar)eE.
3. If Wsm is the angular frequency of transition from mih state to * state, perturbation changes at rapid, rate during 7 and TtA (very small interval of time, then
for the validity of sudden approximation,
'
(a) A 1
(b) A1
.(c) W*,1 = 0 id) WaO.
2(1 0,
5, Diracs expression for B is
(a) c (ax px + arpf + azpt + fimc)
(b) iciaiPj+ctyPs+fhic)
(c) c (,]>,+ayp,+cept)
id) c Cax pi? 4- c??_p| + + ||nc)
Answer in I or 2 sentences:
6. The interaction pictures operator Am is jot from the operator in th Sehrodinger picture Ash by a
transformation. What is It?
?. What is the validity condition for WEB to be good?
. 8. Find the selection rules for dipole approximation.
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fl 0 '
0 -1
|
h |
ro -r |
(b) | |
fl 0"| | ||||
|
2 |
i 0 \ / |
2 |
0 1 4. ' x - component of the orbital angular moment is 4 * Tt is given by s W Deduce express forthe genj-gy SECTION D (2 x 1020 marks) for a one dimensional aniarmomc oa 21. (a) Explain matrix mechanics method of W Obtain ' r slowly varying potential pr . Cb) Discuss how variation method i, us.f . W Driva exp. fcx B tradition e,alUatog energy values of a hydrog" ;;0bability of first order por'm.ttme. 22. W Calculate CG coefficient. iOT *A~K>aKi%= 1*1 ; and m2 = , Qr Jl~ /2 J2 ~ /2* "*I/*-- /5i , AnlordiSerend53510- Or Cb) Derive expr _ f r the inelastic scattering* entum (b) Obtain the plane wave solutions for a Dirac'; total mm relativistic free particle, 19, (a). Show that the towu w operator J2 mmsmiis wMx Jy and Jf. Or (b) Find the eigea values of J , '20, (a) Derive Sam Gordan equation. State the iaadeqaades of the theory, Cr (b; Calculate spia orbit energy from Dirac's '*4 A 19. (al Sho* *at to' j 1 2 *tnntaswJ *** 3044 7 30
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 Bharathiar University 2001 M.Sc Physics Quantum Mechanics -I - Question Paper
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