12 量子物理
Sections
1.Photon and Matter Waves 2.Compton Effect
3.Light as a Probability Wave 4.Electrons and Matter
Waves
5.Schrodinger’s Equation 6.Waves on Strings and
Matter Waves
7.Trapping an Electron 8.Three Electron Traps 9.The Hydrogen Atom
12-1.1 Photon and
Matter Waves ( 光子 和物質波 )
• Light Waves and Photons
s J 10
63 .
6
) energy photon
(
34
h
hf E
f c
The Photoelectric Effect
光電效應
•
First Experiment
(adjusting V)–
the stopping potential Vstop
• Second Experiment (adjusting f)–
the cutoff frequency f0
stop
max
eV
K
The experiment
光電子的最大動能與 光強度無關
低於截止頻率時即使光再 強也不會有光電效應
The plot of V
stopagainst f
The Photoelectric Equation
s J 10
6 . 6
) (
34 stop
max
h
f e e
V h
K
hf Work
functio n
12-1.2 Compton
Effect
momentum) (photon
h c
p hf
康普 吞效 應實 驗圖 表
康普吞效應圖示
mv p
h p
h mc h
mc f
h hf
mc K
K f
h hf
e
X
/
) 1 (
) 1 (
) 1 (
2
2
Energy and momentum
conservation
) cos
1 (
sin sin
0
cos cos
mc h h mv
h mv h
Frequency shift
Compton wavelength
12-1.3 Light as a Probability Wave
The
standard version
The single-photon,
double-slit experiment is a phenomenon which is impossible, absolutely impossible to explain in any classical way, and
which has in it the heart of quantum mechanics - Richard Feynman
The Single-Photon Version
First by Taylor in 1909
The Single-Photon,
Wide-Angle Version
(1992)
Light is generated in the source as photons
Light is absorbed in the detector as photons
Light travels between
source and detector as a probability wave
The postulate
12-1.4 Electrons and Matter Waves
p
h
• The de Broglie wave length
• Experimental verification in 1927
• Iodine molecule beam in 1994
1989 double-slit experiment
7,100,3000, 20,000 and 70,000 electrons
Experimental Verifications
X- ray
Electr on beam
苯環 的中 子繞 射
12-1.5 Schrodinger’s Equation
• Matter waves and the wave function
• The probability (per unit time) is
t
e
iz y x
t z y
x , , , ) ( , , )
(
2ie. *
Complex conjugate
共軛複數
The Schrodinger
Equation from A Simple Wave Function
m k
m p
E
k h
p
kx B
kx A
e z
y x
t z y
x
i t2 / 2
/ /
) cos(
) sin(
) ,
, (
) ,
, ,
(
2 2
2
dx E d m
dx d E m
dx k d
k dx
d
kx B
kx A
2 2 2
2 2 2
2 2 2
2 2
2
2
2 1
1 /
) cos(
) sin(
1D Time-independent
SE
i t m V
i t m
dz E d dy
d dx
d m
dx E d m
2 2
2 2
2 2 2
2 2
2 2
2 2 2
2 2
) 2 (
2
3D Time-dependent SE
12-1.6 Waves on
Strings and Matter
Waves
Confinement of a Wave leads to Quantization –
discrete states and discrete energies
駐波與量子化
Quantization
n = , , ,
L n v
f v n
L 0 1 2
2
= 2
駐波：
number
quantum :
, 3 , 2 , 1
, ) sin(
, 3 , 2 , 1 2
n
n L x
A n y
n n L
n
12-1.7 Trapping an Electron
For a string ：
, 3 , 2 , 1
, 8
/
2 / ,
2 /
/
2 2
2
n mL
h n E
n L
mE h
p h
n
Finding the Quantized
Energies of an infinitely
deep potential energy well
The ground state and
excited states
The Zero- Point
Energy
n can’t be 0
The Energy Levels
能階
, 3 , 2 , 1
, ) (
sin
, 3 , 2 , 1
, ) sin(
, 3 , 2 , 1
, ) sin(
2 2
2
n L x
A n
n L x
A n
n L x
A n y
n n n
The Wave Function and Probability
Density
For astring
The Probability
Density
• Normalization (
歸一 化 )
n2( x ) dx 1
Correspondence principle
(
對應原理 )At large enough quantum
numbers, the predictions of quantum mechanics merge smoothly with those of
classical physics
0 )]
( 8 [
2 2 2
2
x E
h E
m dx
d
pot
A Finite Well
有限位能井The probability
densities and energy
levels
Barrier Tunneling
穿隧效應STM
掃描式穿隧顯微鏡Piezoelectricity of quartz
12-1.8 Three Electron Traps
• Nanocrystallites 硒化鎘奈米 那種顏色的顆粒比較小晶粒
t t
t E
ch c f
2 2 2
8mL h En n
A Quantum Dot
An Artificial Atom
The number of electrons can be controlled
Quantum Corral
量子圍欄
12-1.9 The Hydrogen Atom
• The Energies
, 3
, 2 , 1
ev , 6
. 13 1
8
4 1 4
1
2 2
2 2
0 4
2
0 2
1 0
n n n
h E me
r e r
q U q
n
氫原 子能 階與 光譜 線
Bohr’s Theory of
the Hydrogen Atom
radius) (Bohr
pm 29
. 5 ) 1
(
2 0 2
/ 2
/ 3
