Мартыненко Т.П. и др. Практический курс физики. Квантовая физика. Элементы физики твёрдого тела и ядерной физики
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71
( ~ 0,1 ).
.
+Ze , . (
,
–
).
(
)
2
2
n
aZRhc
E
−
−= , (3.21)
.
, Z.
- 1, L - – 7,5.
,
( ) ( )
−
−
−
=
λ
2
2
2
2
2
1
2
1
n
aZ
n
aZ
R
1
, (3.22)
“1” , “2” –
.
-
- ( ,
…) ( . . 3.4). L -
– L - (L , L …).
(
)
2
2
n
aZR
T
−
=
. (3.21),
T
Z.
.
.
,
.
L
L
m2
e
e
L
⋅=µ (3.23)
- , m – . )1(L +⋅⋅= ll (3.10)
K
α
K
β
K
γ
L
α
L
β
N
M
L
K
E
. 3.4
72
( ) ( )
11
m2
e
e
L
+⋅µ=+⋅=µ llll (3.24)
/10927,0
m2
e
23
e
−
⋅==µ – .
S
µ
S
m
e
e
S
⋅=µ , (3.25)
(
)
(
)
12/12/11ssS +=+⋅= ,
3
S
⋅µ=µ (3.26)
, ,
L
µ
S
µ
,
L
S
.
. . 3.5
.
µ
J
.
L
,
S
,
L
µ
,
S
µ
µ
,
J
.
J
µ=µ .
µ ,
.
. 3.5,
(
)
1jjg +⋅⋅⋅µ=µ , (3.27)
(
)
(
)
(
)
( )
1jj2
11ss1jj
1g
+
+
−
+
+
+
+=
ll
(3.28)
, .
B
,
W,
:
(
)
BBW
Z
µ−=µ−= , (3.29)
Z
µ – Z,
B
. (3.27)
J
S
L
S
µ
L
µ
µ
. 3.
5
73
Jg
m2
e
e
⋅⋅=µ ,
Z
jj
e
Z
e
Z
mgmg
m2
e
Jg
m2
e
⋅⋅µ=⋅=⋅=µ (3.30)
j
mBgW ⋅⋅⋅µ= . (3.31)
.
.
re
EEEE
+
+
=
υ
, (3.32)
E
e
– ;
υ
E –
, ,
; E
r
– .
(3.32) ,
E
:
re
EEE
∆
>>
∆
>>
∆
υ
. . 3.6
.
re
E
EE
∆
+
∆
+
∆
=ω
υ
(3.33)
,
r
E
∆
=ω ,
, ,
.
,
–
.
r
EE
∆
+
∆
=ω
υ
.
2=υ
′′
1=υ
′′
0=υ
′′
2=υ
′
1=υ
′
0=υ
′
E
J
′′
3
2
1
3
2
1
e
E
′
J
′
e
E
′′
. 3.
6
74
–
, .
(3.33).
,
.
.
.
( . 3.7)
.
, ,
. , ,
, ,
. .
3.8
.
,
.
, .
( . 3.8)
. ,
.
:
+υω⋅=
υυ
2
1
E
(3.34)
υ
ω
– :
µ
=ω
υ
k
(3.35)
k – , µ –
:
21
21
mm
mm
+
⋅
=µ (3.36)
m
1
, m
2
– , ,
υ
– :
...2,1,0
=
υ
(3.37)
. 3.7
U(r)
E
d
E
0
r
0
r
ω
2
1
. 3.8
75
(3.34) .
:
1
±
=
υ
∆
.
. –
:
2
2
1
2
1
E +υω⋅⋅κ−+υω⋅=
υυυ
(3.38)
κ
– , ~ 0,01.
(3.38)
υ
,
E
0
( . . 3.8). E
0
. E
d
E
0
.
:
(
)
⋅
⋅
+⋅⋅
=
I
2
1JJ
E
2
r
(3.39)
J – ,
J = 0, 1, 2 … (3.40)
I – ,
:
2
dI ⋅µ= (3.41)
d – ,
µ
–
.
I2
B
2
⋅
=
.
:
(
)
1JJBE
r
+
⋅
⋅
=
.
(3.39)
J.
.
1J2g
+
=
. (3.42)
–
1
J
±
=
∆
.
76
,
( – ),
:
1
,0J
±
=
∆
, , J = 0
.
3.1.
.
(n = 1) (n ).
1i
EEE
−
=
. (3.19)
(Z = 1) RhcE
1
−
=
, 0E
=
∞
, RhcE
i
=
.
e
Rhc
e
E
U
i
i
== , 6,13U
i
=
.
(n = 1)
(n = 2).
Rhc
4
3
)4/11(RhcEEE
12
=−=−= .
4e
Rhc3
e
E
U
1
== , 2,106,13
4
3
U
1
=⋅= .
3.2.
, .
d = 5 .
,
= 41º?
.
:
λ
=
ϕ
msind , m =5,
10561,6
5
6561,0105
m
sind
7
6
−
−
⋅=
⋅⋅
=
ϕ
=λ .
,
, .
n = 2.
(3.20), n = 2, −=
λ
22
n
1
2
1
R
1
,
R
1
4
1
n
1
2
λ
−= ,
77
3
4R
R4
n =
−λ
λ
= .
n = 3 n = 2.
3.3. He ll ,
. He ll
?
He Z = 2. (3.20) He ll :
−=
λ
22
n
1
n
1
R4
1
.
( )
n = 3 n = 2
−=
λ
22
3
1
2
1
R
1
.
.
−=−
9
1
4
1
R
n
1
n
1
R4
22
,
36
1
16
1
n
1
n
1
22
−=− .
n = 4, n = 6.
3.4.
,
, ,
? ,
.
210
E+T+T=T ,
0
–
;
1
2
–
; –
.
0
,
, . . .
n = 2. :
Rhc
4
3
4
1
1RhcEEE
12
=−=−=
, =10,2 .
0
,
, . .
, ,
78
T=T=T
21
.
210
p+p=p ,
0
– ,
1
2
– .
, p=p=p
21
;
0
E+T2=T , p2=p
0
. ,
mT2p = , =
0
/4
Rhc
2
3
E2T
0
== ,
0
=20,4 .
3.5.. , ,
He ll
7,133
=
λ
∆
.
,
( He ll):
−=
λ
22
1
3
1
2
1
R4
1
,
−=
λ
2
2
2
1
1R4
1
,
R
9
51
1
⋅=
λ
, R3
1
2
=
λ
;
R15
22
R3
1
R5
9
21
=−=λ−λ=λ∆ .
17
10097,1
15
22
R
−
⋅=
λ∆⋅
= .
3.6.
, E = 1,51 .
.
( )
n
Rhc
E
2
=
( )
e
n
Rhc
E
2
⋅
= . n
2
=9, n=3.
, l, m, m
s
.
. n
l n (l = 0, 1, … , n-1).
l 2l + 1 m
(m = 0, ±1, ±2, …, ±l). , l m
n
( )
(
)
2
1n
0
nn
2
11n21
12 =⋅
+−+
=+
−
=l
l
.
n, l, m ,
m
s
(m
s
= 1/2, m
s
= –1/2). ,
N = 2n
2
, N = 18.
79
3.7.
,
(
)
(
)
r
e·ar1Ar
α−
+=Ψ , , –
. n
?
,
, (3.2).
,
r:
0
r4
e
E
m2
dr
d
r
dr
d
r
1
0
2
2
2
2
=Ψ⋅
πε
++
Ψ
⋅ .
, :
0arEE
4
ae
r4
em2
r
2
r
a2
ara4
0
2
0
2
2
22
=++
πε
+
πε
+
α
−+α+α+α− . (1)
r, :
( )
( )
0
r
1
4
e
a
m
raEa
m2
E
4
ae
a4
m2
0
22
2
2
0
2
2
2
=⋅
πε
+α−+⋅+α++
πε
+α+α−
, (1) r.
, r
:
( )
0E
4
ae
a4
m2
0
2
2
2
=+
πε
+α+α− . (2)
0Ea
m2
a
22
=⋅+
α⋅⋅
. (3)
( )
0
4
e
a
m
0
22
=
πε
+α− . (4)
(3)
m2
E
22
α
−= ,
(2),
2
0
2
8
me
πε
=α .
( ), :
22
0
2
4
2
0
2
4
22
0
2
4
2
1
h8
me
h32
me
128
me
E ⋅
ε
−=
ε
−=
επ
−= .
(3.8), ,
n = 2.
80
3.8. - ,
. ,
Z.
p - l = 1.
j
j = l+s = 1+1/2 = 3/2.
2
15
2
1
2
3
2
3
J
max
=+= .
⋅=
jmax
mJ
z
,
2
3
,
2
1
,
2
1
,
2
3
m
j
−−= .
,
max
J
Z. ,
min
2
3
=m
j
.
7746,0
15
3
2/15
2/3
cos
min
===θ
°
=
=
θ
2,397746,0arccos
min
.
3.9. , ,
= 3000 . ,
,
.
:
kT
E
egCN
−
⋅⋅=
N – , g –
, – .
(n = 1) g = 2,
6,13RhcE
1
−
=
−
=
(n = 2)
8n2g
2
==
,
4
6,13
4
E
E
1
2
−==
2
3
2
2
3
−
θ
min
0
Z