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Unformatted text preview: θ
θ A L
L and you should then understand the equations,
"
#
"
#
1
2p
1
2p
p2
2
P = 3 A(2L=v ) = 3 A(2L=[p=m ]) = 1 ALm = 3 E
3
V
e
e
e
or P = 2E :
3V So from the previous discussion of 0 we know right away that P / 5=3.
Another way to verify this and also get the constant in the relationship,
is by substituting the above expression for E=V in terms of p5 , and also
F
substituting the earlier expression for p3 in terms of ne. The result is the
F
amazing universal formula
1 3 2=3 h2 n5=3
P = 20 m e
(nonrelativistic electrons).
e
Something dierent happens if the electron gas is so compressed that the
Fermi momentum pF starts approaching mec (i.e. the electron velocity starts
approaching c). Then, the above assumptions Ee = p2=(2me ) and ve = p=me
start breaking down! In the extreme relativistic limit, the above calculation
of P goes over to being exactly the same as we previously did for photons,
so
1
P = 3E
V ) 0 = 1
3 )
139 4 =3 ) P / 4=3 : ...
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This note was uploaded on 12/29/2011 for the course AST 350 taught by Professor Dion during the Fall '09 term at SUNY Stony Brook.
 Fall '09
 dion

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