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

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

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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

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

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

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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

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

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

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