MCQ''s - Time Independent Perturbation Theory Notes | EduRev

: MCQ''s - Time Independent Perturbation Theory Notes | EduRev

 Page 1


Multiple Choice Questions in Basic Quantum Mechanics         1 
 
1 
 
Module 10: Time Independent Perturbation Theory 
 
 
10.1  Consider a 4-fold degenerate state with orthonormal eigenfunctions 
1 2 3 4
, , and u u u u . There is 
a perturbationH . It is given that  
12 21
;0 H H g g and all the other matrix elements are 
zero. Find the splitting and corresponding wavefunctions. 
 
(a)  , ,0,0 gg
 
(b)  2 , ,0,0 gg
 
(c) , ,0,0 gg
 
(d)  ,0,0,0 g
 
                                       
[Answer (a)] 
 
10.2   Consider a 4-fold degenerate state with orthonormal eigenfunctions 
1 2 3 4
, , and u u u u . There 
is a perturbationH . It is given that 
12 21
;0 H H g g ,   and all the other matrix elements are 
zero. Find the wave functions of the split levels. 
 
(a)  
1 2 3 4
, , and u u u u
 
(b) 
1 2 1 2
34
, , and
22
u u u u
uu  
 
(c) 
1 2 1 2
34
22
, , and
22
u u u u
uu  
(d) 
1 2 1 2
34
33
, , and
22
u u u u
uu 
 
                                      [Answer (b)] 
 
10.3  Consider a 4-fold degenerate state with orthonormal eigenfunctions 
1 2 3 4
, , and u u u u . There is 
a perturbationH . It is given that 
11 22
2 H H g ,  
12 21
H H g and all the other matrix 
elements are zero. Find the splitting and corresponding wavefunctions. 
 
(a)  , ,0,0 gg
 
(b)  2 , ,0,0 gg
 
(c) 3 , ,0,0 gg
 
(d)  4 , ,0,0 gg
 
                                       
[Answer (c)] 
 
 
 
 
Page 2


Multiple Choice Questions in Basic Quantum Mechanics         1 
 
1 
 
Module 10: Time Independent Perturbation Theory 
 
 
10.1  Consider a 4-fold degenerate state with orthonormal eigenfunctions 
1 2 3 4
, , and u u u u . There is 
a perturbationH . It is given that  
12 21
;0 H H g g and all the other matrix elements are 
zero. Find the splitting and corresponding wavefunctions. 
 
(a)  , ,0,0 gg
 
(b)  2 , ,0,0 gg
 
(c) , ,0,0 gg
 
(d)  ,0,0,0 g
 
                                       
[Answer (a)] 
 
10.2   Consider a 4-fold degenerate state with orthonormal eigenfunctions 
1 2 3 4
, , and u u u u . There 
is a perturbationH . It is given that 
12 21
;0 H H g g ,   and all the other matrix elements are 
zero. Find the wave functions of the split levels. 
 
(a)  
1 2 3 4
, , and u u u u
 
(b) 
1 2 1 2
34
, , and
22
u u u u
uu  
 
(c) 
1 2 1 2
34
22
, , and
22
u u u u
uu  
(d) 
1 2 1 2
34
33
, , and
22
u u u u
uu 
 
                                      [Answer (b)] 
 
10.3  Consider a 4-fold degenerate state with orthonormal eigenfunctions 
1 2 3 4
, , and u u u u . There is 
a perturbationH . It is given that 
11 22
2 H H g ,  
12 21
H H g and all the other matrix 
elements are zero. Find the splitting and corresponding wavefunctions. 
 
(a)  , ,0,0 gg
 
(b)  2 , ,0,0 gg
 
(c) 3 , ,0,0 gg
 
(d)  4 , ,0,0 gg
 
                                       
[Answer (c)] 
 
 
 
 
Multiple Choice Questions in Basic Quantum Mechanics         2 
 
2 
 
10.4   Consider a 4-fold degenerate state with orthonormal eigenfunctions 
1 2 3 4
, , and u u u u . There 
is a perturbationH . It is given that
11 22
2 H H g ,  
12 21
H H g and all the other matrix 
elements are zero. Find the wave functions of the split levels. 
 
(a)  
1 2 3 4
, , and u u u u
 
(b) 
1 2 1 2
34
, , and
22
u u u u
uu  
 
(c) 
1 2 1 2
34
22
, , and
22
u u u u
uu  
(d) 
1 2 1 2
34
33
, , and
22
u u u u
uu 
 
                                      [Answer (b)] 
 
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