普通物理学第七版 第十三章 早期量子论和量子力学基础

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nh 42mrn2
me 4 402h3n3
�13-5
L.V. de Broglie 1892�1986
Ep
E mc2 h p mv h
m0v
hh h
v2
p mv m0v
1 c2
(de Broglie wave) (matter wave)
v c
+d E d E d
a (T )
E
E
0 a(T ) 1
1 a(T ) 1
1100K
M 1(T ) a1(T )
M 2(T ) a2(T )
M 0(T )
1. �J. Stefan & L. Boltzmann
M0(T)
M0(T )
0
nk n>k (n=k+1k+2, )
R
n>k (n=k+1k+2, ) k n
Lyman) k =1
Balmer) k = 2
~
R(
1 22
1 n2
)
n 3,4,5
Paschen) k = 3
k = 4 k = 5
1. � � �
1 2
2.
1
vn
Et
)
(MBorn)
r, t 2 r, t * r, t
2
N N 2
t
r
dV
r, t 2dV
N dV
dN N r, t 2dV
---- ""
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(
r
,
t
)
2
dV
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l
*
(
r,
t
)
(r
,
t
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1 2 ,n
C1 1 C2 2 Cnn Cii
4. E t 2
E
t
13-11 0.01 kg0.5 cm
x 5 103m
px mvx
v x
2mx
1.05 1030 m
s
13-12 10 kV 0.01 cm
x 0.01cm
vx 2mx 0.58m s
v 2eU 6 107m/s m
vx v
c
c
cc
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X
13-4 0 0.02nmX90
(1) X(2) (3)
(1) X
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0 0.0224nm
(2)
h0 m0c2 h mc 2
mc 2
m0c2
hc 0
hc
hc 0
13-10 ,(k=1)
2 a 4.05�10-10 m
a sin k , k 1
h
mv
m m0
h
h
5.14 107 m s
m0v m0a sin
�13-6
x, y, z
----
px , py , pz
----
� W.Heisenberg� d
13-2 �
C1
2hc2 , x
hc kT
hc d x 2kT
d k Tx2 d hc
M0(x,T )
C1k 4T 4 h4c4
x3 ex 1
M0(T )
0
M 0(T )d
C1k 4T 4 h4c4
0
e
x3 x
1
d
x
n0
x e3 (n1) x dx
0
C1k 4T 4 h4c4
i
2
P12
1
2
2
1
2
2
2
1* 2
1
* 2
2n
S.HarocheD.J.Wineland 2012
�13-8 1.
(
x,
t
)
0e
i(
px
x Et
)
(
x,
t
)
0e
i
(
px
x Et
)
( x, t ) i E ( x, t )
t
E px2 2m
i f (t) 1 E t f (t)
i Et
f (t) e
----E
2 2m
2
(r
)
U
(r )(r )
1 (r )
E
2
2m 2
(E
U
) 0
----
(r , t )
(r )
f
(t)
(r )
e
i
Et
(r ,
t)
(r , t )
2
|
(r )
e
i
Et
|2
*
(r )e
x d d sin 1
px p tan 1 p sin 1
x px d p sin 1
p h
x px h
px p sin 1 x px h
x px h y py h
z pz h
1.
2. (1) ""(2)
3. x x, p p ( L>> )
�13-1 �13-2 �13-3 �13-4 �13-5 �13-6 �13-7 �13-8 �13-9 �13-10 �13-11
�13-1
=
M(T)
[W m2]
M
M (T
)
dM (T d
)
[W m3]
a (T )
-- --
rn -e m mp +e
En
2
3
L
mv n rn
n
h 2
n
n = 123
�
vn
rn mp +e
-e m En
r1
0h2 me 2
a0
0.053nm
�
� � �
13-5 12.5 eV
n = 3
31 32 21
1.6 1012 J 10 MeV
1MeV
�13-7
ESchrodinger1925
y( x, t )
y0 cos 2(t
i 2(t x )
x)
y( x, t) y0e
E , h
h
P
x E p
(
x,
t
)
0e
i
(
Et
px
)
(r ,
t
)
0e
i(
p r
d M 0(T ) 0 d m
hc
5(1 e mkT )
hc
mkT
hc
5(1 e mkT )
hc
mkT
hc x
mkT
x 5(1 e x )
x 4.9651 hc
mT 4.9651k b
b hc 2.8978 103 m K 4.9651k
�13-2
h m0v
----
13-7 U1=150VU2=10000V
1 2
m0v 2
eU
2eU v
m0
h h 1 p 2m0e U
U1=150VU2=10000V 1=0.1nm2=0.0123nm
13-8 m=0.05 kgv=300 m/s
13-9 mn=1.67�10-27kg
1. U im I
2.
U = 0 I 0 Ua Ua
Ua
1 2
mv
2 m
eUa
(1)
(2)
3.
0
/(1014Hz) A /eV
10.95 7.73 5.53 5.44 5.15 4.69
4.54 3.20 2.29 2.25 2.13 1.94
M0 (T
)d
T
4
=5.67�10- 8 W/m2�K4----
2. W. Wien
m
T
Tm b
b= 2.897�10-3 m�K ----
13-1 1m490nm
2 3 (RS=6.96�108 m RE=6.37�106 md =1.496�1011 m)
m T b
i
E
t (r )e
i
Et
(r
)
2
(r )
----
�13-9
potential well
10.7 1016 J 6.66 103eV
(3)
h
0 pe cos
0
h
pe sin
pe
h(
2 20 2 20
)1
2
4.44 1023kg m
s
cos h 0.753 0 pe
419
*�13-4
~ 1
~
1 R( k 2
1 n2
)
T(k)
T(n)
13-6 n k = n-1 n n
me4 1
1 me4 2n 1
n1,n
802h3
(n
1)2
n2
802h3
n2(n 1)2
n
me4 2
me 4
n1,n 802h3 n3 402h3n3
vn 2rn
mv n rn 2mrn2
nh 42mrn2
rn
n2
(
0h2 me 2
M0(,T )
� () ----""
, 2, 3, , n n
=h ----
M0 ( ,T ) 2hc2 5
1
hc
e kT 1
2 2 h M0 (,T ) c2 eh / kT 1
(Max Karl Ernst Ludwig Planck 18581947) 1918
1 4(3)2
0.88 102 J
(m2 s)
N I 5.5 1016 2.6 1016 (m2 s)
2.1
�13-3
X
1922�1923X X ----
1927
�
�
1. 0 0
2. = - 0
3.
4.
-0
1925�1926
T
b m
2.897 103 490 109
5.9 103 (K)
M0 T 4 5.67 108 (5.9 103 )4 6.9 107 (W/m2 )
PS M0 4RS2 6.9 107 4 (0.7 109 )2 4.2 1026 (W)
PE
PS 4d 2
2 y2
2 z 2
2 2 U ( x, y, z, t) i
2m
t
�
�
3. U
U r 0 U r 1 e2
40 r
(x, y, z,t) (x, y, z) f (t)
2 2m
2
(r
)
U
(r )(r )
1 (r )
i f (t) t
1 f (t)
1.50 103 W
d >> RE
RE
S
E d
PE PERE2 1.91 1017 W
1.
M
(T
)
C1
5e
C2 T
2. �
�
M (T ) C3 4T
----""
3.
�
M0 ( ,T ) 2hc2 5
1
hc
e kT 1
h 6.626 069 3 1034 J s
T=300K
X
�
1927 CJDavisson LHGermer
d 2.15 1010m
U 54V
50
h
h
k k
m0v
2m0eU
d
� G.P. 1928G.P.
1929 1937 G.P.
1960(C. Jonsson)
1933(E.Ruska) X 10 nm 1986
X ----
1. X
� X"" keV) --------
� X"" eV---- X "" " "
2.
X"" ""
h0 m0c2 h mc 2
m
h0 c
e0
h c
e
mv
m0
1
v2 c2
(mv )2 ( h0 )2 ( h )2 2( h0 )( h )cos
13-13 10-10 m
r 1010m
v p 1 5.8105m/s m m 2r
106 m/s
13-14 10-14 m
r 1014m
p 0.53 1020kg m s 2r
p p 0.53 1020kg m s
Ek E E0 p2c2 m02c4 m0c2
4. 10-9 s
A (work function)
,
A
(1)
h
(2) ""
(3)
h
1 2
mvm2
A
eUa
A
h
1 2
mv
2 m
A
eUa
A
�
�
�
� < A/h
0
A h
A
h
m
c2
Hale Waihona Puke Baidu
h c2
m0 0
h h
p mc
c
400nm
300nm
13-3 P =1 Wd =3 m
r =0.5�10-10 m
A=1.8 eV
1
2
589.3nm
(1) d
P
r 2 4d 2
P
7 1023
W
t A 4000s P
(2)
h hc 3.4 1019 J 2.1eV
3 m
I
P 4d 2
6 n0 (n 1)4
C1k 4T 4 h4c4
4 15
T 4
0
x3 ex
1
d
x
0
ex x3 1 ex
d
x
ex x3 enx d x
0 n0
0
x 3e(n1) x
d
x
(n
6 1)4
2k 4 h3c2
4 15
5.6693 108
W/(m2
K4)
� M0(T ) T 4 m m
2 ( x, t ) x 2
px2 2
( x, t )
2.
U(x, t)
E px2 U ( x, t ) 2m
i
t
( x, t )
[
2 2m
2 x 2
U ( x, t)] ( x, t)
2 2m
2 ( x2
2 y2
2 z 2
) U(x,
y, z, t)
i
t
2
2 x 2