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1
Two neutrons are in an infinite
square well with 2.0 .
What is the minimum total
energy that the system can
have? (Neutrons, like
electrons, have antisymmetric
wave functions. Ignore spin.)
L fm

Solution
2
2 2
2
15
15
2
Using
( 1,2,3,...) (1)
8
1,2, 4.136 10 . ,
939.6 , 2.0 10
in eq.(1), we get
n
n h
E n
mL
Put
n h X eV s
MeV
m L X m
c
3
15 2
1
15 2
2
30 2 2
30 2
2
2 2
2
6
2
10 2
2
2
10 2 2
2
(4.136 10 . )
8 939.6 (2.0 10 )
17.11 10 .
7516.8 4 10
17.11 .
.
30067.2 10
5.69 10 .
5.69 10 .
X eV s
E
MeV
X X X m
c
X eV s
MeV
X X m
c
XeV s
eV m
X
c
X eV s
m
c
X eV s Xc
m











10 2
8 2
1 2
6
5.69 10 .
(2.998 10 )
51.14 10
51.14
X eV s X
m
X
s
E
m
X eV
MeV
4
2 1
1 2
1 2
,
4 4 51.14
204.56
51.14
204.56 255.7
255.7
Now
E XE X MeV
MeV
E E MeV
MeV MeV
E E E MeV
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Paul 7.44.doc

  • 1. 1 Two neutrons are in an infinite square well with 2.0 . What is the minimum total energy that the system can have? (Neutrons, like electrons, have antisymmetric wave functions. Ignore spin.) L fm Solution
  • 2. 2 2 2 2 15 15 2 Using ( 1,2,3,...) (1) 8 1,2, 4.136 10 . , 939.6 , 2.0 10 in eq.(1), we get n n h E n mL Put n h X eV s MeV m L X m c
  • 3. 3 15 2 1 15 2 2 30 2 2 30 2 2 2 2 2 6 2 10 2 2 2 10 2 2 2 (4.136 10 . ) 8 939.6 (2.0 10 ) 17.11 10 . 7516.8 4 10 17.11 . . 30067.2 10 5.69 10 . 5.69 10 . X eV s E MeV X X X m c X eV s MeV X X m c XeV s eV m X c X eV s m c X eV s Xc m 10 2 8 2 1 2 6 5.69 10 . (2.998 10 ) 51.14 10 51.14 X eV s X m X s E m X eV MeV
  • 4. 4 2 1 1 2 1 2 , 4 4 51.14 204.56 51.14 204.56 255.7 255.7 Now E XE X MeV MeV E E MeV MeV MeV E E E MeV