Old Exam Papers Dec. 2010 - Video

5. (a) Determine the eigenvalues and eigenfunctions of a
particle placed in one dimensional box of side
L b0 ? x ? Lg.
8
,dfoeh; Hkqtk L ds ckWDl esa fLFkr ,d d.k ds
vkbxsu eku ,oa vkbxsu Qyu Kkr dhft;sA
b g 8
L 0 ? x ? L
(b) Find the lowest energy of an electron confined to
move in one dimensional box of length 1Å. 2
1Å yEckbZ ds ,dfoeh; foHko ckWDl esa lhfer xfr
djus okys bysDVªkWu dh U;wure ÅtkZ dk eku Kkr
dhft;sA 2
6. Obtain the solution of Schrödinger equation in various
regions of one dimensional rectangular potential barrier and
hence find the expression for transmission coefficient.
Define tunnel effect. 10
,dfoeh; vk;rkdkj foHko jksf/kdk ds fofHkUu {ks=ksa esa JksfMaxj
lehdj.k ds gy izkIr dhft;s rFkk ikjxeu xq.kkad ds fy,
O;atd izkIr dhft;sA lqjax izHkko dks ifjHkkf"kr dhft;sA 10
7. (a) What is transmission resonance ? Explain Ramsauer
Townsend effect with help of this. 5
Papers (A) (December) 2010
(479)
ikjxeu vuqukn fdls dgrs gSa \ bldh lgk;rk ls
jkelkSj Vkmuls.M izHkko dks le>kb;sA 5
(b) Write the eigenvalues and eigenfunctions of a
particle moving in an infinitely deep potential well in
first four states. Represent the wave functions for
first four states graphically. 5
,d vuUr xgjkbZ ds foHko dwi esa xfr dj jgs d.k dh
izFke pkj voLFkkvksa ds fy, vkbxsu eku lar vkbxsu
Qyu fyf[k;sA izFke pkj voLFkkvksa ds fy, rjax Qyuksa
dks vkjsf[kr dhft;sA 5
8. (a) What is zero point energy ? How does the
uncertainty principle help in explaining the concept
of zero point energy ? 5
'kwU; fcUnq ÅtkZ D;k gksrh gS \ vfuf'prrk dk fl)kUr
'kwU; fcUnq ÅtkZ dh O;k[;k djus esa fdl izdkj lgk;rk
djrk gS \ 5
(b) What is parity ? Give the parity of symmetric and
antisymmetric wave functions. Prove that the eigen
values of parity operator are ?1. 5
lerk fdls dgrs gSa \ lefer rFkk izfrlefer rjax
Qyuksa dh lerk fyf[k;sA fl) dhft;s fd lerk ladkjd
ds vkbxsu eku ?1 gksrs gSaA 5
600 4 PH-09 PH-09 5 PTO