Смирнов В.П. Курс статистической физики. Конспект лекций
Подождите немного. Документ загружается.
T T
r
τ 1 Z
o
Z
o
=
e
N
∞
X
m=−∞
e
−
m
2
τ
=
e
N
Z
∞
m=−∞
e
−
m
2
τ
dm =
e
N
(πτ)
1/2
=
2πe
hN
(2πIkT )
1/2
,
E = kT
2
N
∂ ln Z
o
∂T
≈
1
2
NkT, C =
1
2
Nk,
Z
o
E C
T T
r
τ 1
Z
o
≈
e
hN
(1 + 2e
−
1
τ
),
E = kT
2
N
∂ ln Z
o
∂T
≈ 2NkT
r
e
−
T
r
T
= 2NkT
r
e
−
1
τ
,
C =
∂E
∂T
= 2Nk
T
r
T
2
e
−
T
r
T
= 2Nkτ
−2
e
−
1
τ
,
T
r
T
r
N
2
O
2
H
2
HCl HBr
T
r
K 2.86 2.07 85.4 15.2 12.1
L
m V = L
3
E
n
= E
n
1
,n
2
,n
3
=
π
2
~
2
2mL
2
(n
2
1
+ n
2
2
+ n
2
3
), (n = (n
1
, n
2
, n
3
), n
1
, n
2
, n
3
= 1, 2, ...).
Z
Z = z
N
o
, z
o
=
e
N
"
∞
X
n
1
=1
exp
−
T
tr
T
n
2
1
#
3
=
e
N
"
∞
X
n=1
exp
−
n
2
τ
#
3
,
T
tr
=
π
2
~
2
2mL
2
k
τ =
T
T
tr
L = 1 T
tr
. 10
−15
K
T T
tr
τ 1
∞
X
n=1
exp
−
n
2
τ
≈
Z
∞
0
exp
−
n
2
τ
dn =
1
2
(πτ )
1/2
Z ≈
(2πmkT )
3/2
h
3
eV
N
N
H =
N
X
i=1
H
i
,
H
i
i
Z = Z
N
o
Z
o
3n n
n 3n
q
1
= X q
2
= Y
q
3
= Z
q
4
= ϕ q
5
= θ q
6
= ψ
q
4
q
5
3n − 6 3n −5
U(q) =
3n
X
j=7(6)
c
j
q
2
j
.
1
2
kT
1
2
k
1
2
kT
1
2
k
kT k
1
2
kT
1
2
kT
1
2
k
kT k
n (3n−3)kT
(3n −3)k (3n −
5
2
)kT
(3n −
5
2
)k C =
3
2
C =
7
2
k
3
2
k
5
2
k
7
2
k
T < T
o
E
(el)
i
∆E
(el)
= E
(el)
1
−E
(el)
0
kT T T
el
T
el
≡
∆E
(el)
k
E
(el)
1
E
(el)
0
T
el
∼ 200 K
∆E
1
∆E
2
= E
(el)
2
− E
(el)
1
Z
(el)
o
= g
0
e
−
E
(el)
0
kT
+ g
1
e
−
E
(el)
1
kT
= g
0
e
−
E
(el)
0
T
el
∆E
1
T
1 +
g
1
g
0
e
−
T
el
T
,
g
0
g
1
E
N
= kT
2
∂ ln Z
(el)
0
∂T
= kT
el
E
(el)
0
∆E
1
+
g
1
g
0
kT
el
e
−
T
el
T
1 +
g
1
g
0
e
−
T
el
T
C
N
=
1
N
∂E
∂T
= k
g
1
g
0
T
el
T
2
e
−
T
el
T
1 +
g
1
g
0
e
−
T
el
T
2
= k
g
0
g
1
T
el
T
2
e
T
el
T
g
0
g
1
e
T
el
T
+ 1
2
.
C/N
τ =
T
T
el
ε
{l
i
}
= ε
l
1
+ ε
l
2
+ ··· + ε
l
N
.
ε
l
i
l
i
i
λ = exp(iα)
ψ(q
2
, q
1
, q
3
, ..., q
N
) = λψ(q
1
, q
2
, q
3
, ..., q
N
)
ψ(q
1
, q
2
, q
3
, ..., q
N
) = λψ(q
2
, q
1
, q
3
, ..., q
N
) = λ
2
ψ(q
1
, q
2
, q
3
, ..., q
N
),
λ
2
= 1 λ = ±1
λ = −1
λ = 1
ψ
(A)
=
X
p
p
ˆ
P ψ
l
1
(q
1
)ψ
l
2
(q
2
)...ψ
l
N
(q
N
)
p
ˆ
P p
p
= ±1
p
ψ
(S)
=
X
p
ˆ
P ψ
l
1
(q
1
)ψ
l
2
(q
2
)...ψ
l
N
(q
N
).
ψ
(A)
ψ
(A)
=
ψ
l
1
(q
1
) ψ
l
1
(q
2
) . . . ψ
l
1
(q
N
)
ψ
l
2
(q
1
) ψ
l
2
(q
2
) . . . ψ
l
2
(q
N
)
··· ··· ··· ···
ψ
l
N
(q
1
) ψ
l
N
(q
2
) . . . ψ
l
N
(q
N
)
.
ψ
l
1
= ψ
l
2
l
1
= l
2
ψ
(A)
≡ 0
l
1
= l
2
= l
3
ψ
(S)
6= 0
l ε
l
n
l
ρ = exp
Ω + µN − E
{l
i
},N
kT
;
N =
X
l
n
l
, E
{l
i
},N
=
X
l
ε
l
n
l
; Ω =
X
l
Ω
l
,
ρ = exp
P
l
Ω
l
+ (µ − ε
l
)n
l
kT
=
Y
l
ρ
l,n
l
.
ρ
l,n
l
= exp
Ω
l
+ (µ − ε
l
)n
l
kT
l n
l
ρ ρ
l,n
l
l l l
n
l
ε
l
l
X
n
l
ρ
l,n
l
= 1, exp
Ω
l
kT
X
n
l
exp
µ −
l
kT
n
l
= 1,
Ω
l
= −kT ln
X
n
l
exp
µ −
l
kT
n
l
.
l
n
l
= −
∂Ω
l
∂µ
=
X
n
l
n
l
exp
Ω
l
+ (µ − ε
l
)n
l
kT
.
Ω
Ω =
X
l
Ω
l
= −kT
X
l
ln
X
n
l
exp
µ − ε
l
kT
n
l
.
T, V, µ
n
l
= 0, 1
1
X
n
l
=0
e
µ − ε
l
kT
n
l
= 1 + e
µ − ε
l
kT
, Ω = −kT
X
l
ln
1 + e
µ − ε
l
kT
.
f
(F −D)
l
= −
∂Ω
l
∂µ
=
e
µ − ε
l
kT
+ 1
−1
= n
l
l
−
∂Ω
∂µ
=
X
l
e
µ − ε
l
kT
+ 1
−1
=
X
i
g
i
e
µ − ε
i
kT
+ 1
−1
= N
µ = µ(T, V, N) T, V, µ
T, V, N
E = Ω + T S + µN =
X
l
f
(F −D)
l
ε
l
,
f
(F −D)
l
=
n
l
T = 0
ε = ε
F
= µ
f
(F −D)
l
(ε
l
) µ
f
(F −D)
l
= n
l
n
l
= 0, 1, 2, ...
∞
X
n
l
=0
e
µ − ε
l
kT
n
l
=
1 − e
µ − ε
l
kT
−1
, Ω = kT
X
l
ln
1 − e
µ − ε
l
kT
.
f
(B−E)
l
= −
∂Ω
l
∂µ
=
exp
ε
l
− µ
kT
− 1
−1
= n
l
l n
l
≥ 0
exp
ε
l
−µ
kT
≥ 1 µ ≤ ε
l
µ
µ ≤ ε
0
−
∂Ω
∂µ
=
X
l
exp
ε
l
− µ
kT
− 1
−1
=
X
i
g
i
exp
ε
i
− µ
kT
− 1
−1
= N
µ = µ(T, V, N) T, V, µ
T, V, N