Old Exam Papers June 2012 (Set 2)

particle within box for n = 1, 2 and 3. How probability results
differ from classical view ? 10
,dfoeh; ckWDl esa fLFkr d.k ds fy, JksfMaxj lehdj.k dks gy
dj ÅtkZ ds vkbxu eku o vkbxu Qyu Kkr dhft;sA fdlh
d.k dks ckWDl ds vUnj ik;s tkus dh izkf;drk dks
n = 1, 2 ,oa 3 ij n'kkZb;s rFkk crkb;s fd ;g izkf;drk dk
eku] fpjlEer fl)kUr ls fdl rjg fHkUu gS \ 10
6. What is potential barrier ? Using quantum mechanics prove
that there exists a finite probability of transmission of a
particle through a barrier of height V0bg x when the energy
E of the particle is less than V 0 . Discuss decay of alpha
particle. 10
foHko izkphj D;k gksrh gS \ DokaVe ;kaf=dh dh lgk;rk ls fl)
dhft;s fd izkphj dh Å¡pkbZ V 0 ls de ÅtkZ (E) okys d.k dh]
izkphj ls ikjxeu dh lnSo ,d ifjfer izkf;drk gksrh gSA
vYQk d.kksa ds {k; dh foospuk dhft;sA 10
7. (a) Solve the Schrödinger's equation for linear harmonic
oscillator and obtain the energy eigenvalue. 7
fdlh ,dfoeh; ljy vkorhZ nksyd ds fy, JksfMaxj
lehdj.k dks gy dhft;s vkSj ÅtkZ ds vkbxu eku izkIr
dhft;sA 7
200 4 PH-09
mechanics. Derive and discuss the need and justification
of Schrödinger wave equation. What is a wave function ?
What is meant by normalised wave functions ? Discuss
physical significance of wave functions. 3+4+1+1+1
DokaVe ;kaf=dh ds eq[; vfHkx`ghrksa dks fyf[k;sA JksfMaxj lehdj.k
dh vko';drk o lkFkZdrk dks le>kb;sA rjax Qyu D;k
gS \ izlkekU;hÑr rjax Qyu dk D;k vFkZ gS \ rjax Qyu
dh HkkSfrdh lkFkZdrk le>kb;sA 3+4+1+1+1
4. (a) Define linear and Hermitian operators in quantum
mechnics and prove that eigenvalue of Hermitian
operator are real. 6
DokaVe ;kaf=dh esa js[kh; ,oa gfeZVh ladkjd dks ifjHkkf"kr
dj fl) dhft;s fd ,d gfeZVh ladkjd ds vkbxu eku
okLrfod gksrs gSaA 6
(b) Discuss Boundary and Continuity conditions on the
wave functions. 4
rjax Qyu ij lhekUr ,oa lkUrR; izfrcU/kksa dks
le>kb;sA 4
5. Solve the Schrödinger equation for a particle situated in
one dimensional box and determine its energy eigenvalue
and eigenfunction. Draw the graph of probability of finding
PH-09 3 PTO