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u JvwLQNxMLGT(oFLGTVUWaLo+knfqrT#_sLQthNsknm R ln x dx = x ln x − x e(]yLQWXT(L^z8tnNOgh{
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n −x
n
0
0
0
x
0
0
0
0
φ00 (x) = Coshφ(x) , φ(0) = 1
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p
E = |~
‹hLQNOLGWaTFi8knPSR#_cxLQNOo(LQT0YGe p| c + m c
p
Z
E ≈ |~
p| c = |~
p|c
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x WXNoZ
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S = −kB hln Pα i = −kB
X
Pα ln Pα
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F (T, V, N ) = −k T ln Z
= U − T S.
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X
α
α
kanonisch
B
e−β(Eα −µNα )
Zgrosskanonisch (T, V, µ) =
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R(LGN
α
J = −kB T ln Zgrosskanonisch
J(T, V, µ) = U − T S − µ hN i
B
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(nk − n)2
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d
1
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x
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x
d
dx (1 − x)2
1
1
d
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1
2
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−
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=
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Lw¾¼T(LGNthWXL
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ε =ε ≡k T
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−
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1
2
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