The dual nature of light,particle and wave
光的波粒二象性
particle wave
（ energy） （ frequency）
（ momentum） （ wavelength）
?E
??P
?h
These two natures are connected by h,
)1(??? hE ?
)2(/ ?
?
?
??
h
C
hCEP ???
22
0
2 )( cPEE ??
4.德布罗意波、波粒二象性
（ De Br glie wave,Wave-Particle Dualism ） ?
De Broglie assumed that the wavelength
of predicted matter waves was given by
the same relationship that held for light
namely,or
λ= h / P
u?
Z
X
Y
E?
H? particle
wave
which connects the wavelength of a
light wave with the momentum of the
De Broglie wave
associated photons,
De Broglie predicted that the wavelength of
matter waves would also be given by
λ= h / P
where P would now be the momentum of the
particle of matter,
De Broglie wave
Example 1,What wavelength is predicted by
De Broglie wave for a bullet whose mass is
m0=0.05kg and velocity is v=300m/s?
Solve,∵ V << C
)(104.4
3 0 005.0
1063.6 3534
0
m
Vm
h ?? ??
?
???? = 4.4?10-24(?)
Example 1,What wavelength is predicted by
De Broglie wave for a bullet whose mass is
m0=0.05kg and velocity is v=300m/s?
Solve,∵ V << C
)(104.4
3 0 005.0
1063.6 3534
0
m
Vm
h ?? ??
?
???? 即 4.4?10-24?
U
B
K
发射电
子阴级 加速电极
e
m0 V?
Exp 2,What wavelength is predicted by De Broglie
wave for a beam of electrons whose kinetic energy is
eU and velocity is v? （ V??C）
eUVm ?20
2
1?
From the law of
conservation of energy,
U
B
K
发射电
子阴级
加
速
电
极
0
2
m
eU
V ??
P
h??
Uem
h
02
?
?
? A
U
3.12
Vm
h
0
?
e
m0 V?
or )(103.12 10 m
U
???? or
U
3.12?? ?
When U=100(V),3.123.12 ??
U
? (?)
eUVm ?2021?
De Broglie wavelength
follows from
G
Ni单晶
电
流
计
Demonstration of De Broglie wave
1) C,J,Davisson and L,H,Germer Test
戴维逊 --革末实验
Figure shows the apparatus of Davisson and Germer,
实验装置,
U
?
?
M
IB
K
发射电
子阴级
加
速
电
极
1） C,J,Davisson and L,H,Germer Test
实验装置,
U
I
a=0.215nm d=0.0908nm U=54(v)
U
G
Ni单晶
电
流
计 ?
?
M
IB
K
发射电
子阴级
加
速
电
极
Ni单晶
d
a
φ =50°
suppose
De Broglie wavelength of electron waves would be
given by
)9(3.12
2 0
?
?
?? A
UUem
h
?
From Bragg’s law ?? kd ?s in2
)10(
2
s in2
0
?
Uem
h
kd ??
?.321 ???k
φ=51o
实验装置,
G
Ni单晶
电
流
计 U
IB
K
发射电
子阴级
加
速
电
极
electrons
are waves,
Experi-
mental value
is given by
φ=50o,
This is
excellent
agreement,
?
?
M
2) G.P,Thomson electron diffraction test
1927 年汤姆逊（ G·P·Thomson）以 600伏慢电子
(?=0.5?)射向铝箔，也得到了像 X射线衍射一样的衍
射，再次发现了电子的波动性。
1937年戴维逊与 GP汤姆逊共获当年诺贝尔奖,
G·P·Thomson为电子发现人 J·J·Thmson的儿子,
尔后人们又发现了质子、中子的衍射,
3) Electron double-slit diffraction test 电子双缝实验
1961年琼森（ Claus J?nsson）将一束电子加速
到 50Kev，让其通过一缝宽为 a=0.5?10-6m，间隔
为 d=2.0?10-6m的双缝,当电子撞击荧光屏时,发现
了类似于光的双缝衍射的图样,
大量电子一次性 行为
电子双缝实验 — 一个电子多次重复性行为
Scanning tunnelling microscope
扫描隧道显微镜
扫描隧道显微镜中的原子形象
中文书,19— 15,
19— 16,
外文书,48— 1,