经典物理的困惑,
量子物理
（ Quantum Physics）
2） 1990年，“紫外灾难”；
1） 1887年,A.A.Michelson-E.W.Morley实验否
定了绝对参考系的存在；
光是电磁波还是微粒？
1,黑体辐射、普朗克量子假说
（ Black-body Radiation,Planck?s Quantum Supposition）
热辐射
实 验
3） 1896年，首次发现放射性现象。
1） Heat Radiation （ 热辐射）
Experiment shows,
火
炉
600度 1000度 400度 Radiation relates to
temperature,
2） black body (黑体 )
black-body radiation (黑体辐射 )
抛光的铜镜表面吸收率,
一般金属表面吸收率,
煤烟吸收率,
02.0?总a
8.06.0 ??总a
98.095.0 ??总a Let us construct cavity in a metal block,through
the wall of which a small hole is drilled,This small
hole is called a black body,(a总 =1)
如远处不点灯的窗
若室内点灯
（是自身辐射）
a） spectral radiancy (单色辐出度 )
The quantity M(?T) is the rate at which energy is
radiated per unit time,per unit wavelength and
per unit area of surface for wavelengths lying in
the interval ? to ?+d? at the temperature T,
黑体
?
?
? d
dMM
T ?).(
).( 3?mWa总 =1
显然，它是波长和温度的函数
b) radiancy (辐出度 )
The appropriate quantity M(T) is the rate at which
energy is radiated per unit time and per unit area
of surface at the temperature T,
?dM
?d
黑体
).( 2?mW
a总 =1
显然，它是温度的函数,
b) radiancy (辐出度 )
单位时间内从物体单位面积上所辐射的各种
波长的总的辐射能，用 M（ T）表示。
TM
? ?? 0 ).()( ?? dMM TT
3) Studing black-body radiation experimentally
equipment 实验装置
A
L1
B P
L2 C
黑体
平行光管 三棱镜
测量系统
The law about black-body radiation黑体辐射规律
1.0 2.0 3.0 4.0 5.0
20
30
10
40
50
60
?(nm)
).( 11)(0 ?? mcmwM T ??
2200K
2000K
1800K
1600K
a) J.Stefan—Ludwig
Boltzmarn law,
4
)(0 TM T ??
mKw /1067.5 8????
J.Stefan—Ludwig
Boltzmarn constant
M0(T) depend only on the temperature and are
quite independent of the material and of the shape
and size of the cavity,
The law about black-body radiation
b)Wien displacement law
(维恩位移定律 ),
bT m ??
Kmb,108 9 8.2 3???
m?
,wavelength for
peak value
T,absolute temperature
火
炉
1000度 2000度 800度
炉火纯青
注意：以上两规律只适用于黑体，对非黑体只
近似成立。
1.0 2.0 3.0 4.0 5.0
20
30
10
40
50
60
?(nm)
).( 11)(0 ?? mcmwM T ??
2200K
2000K
1800K
1600K
Exp,The sun is a black-body,It?s wavelength fom
peak valueλm=5100A on the earth,Find the
surface temperature and radiancy,
例,太阳可以看成黑体，地球上测出其峰值波长
为 ?m=5100?，则其表面温度和辐出度为多少？
From
bT m ??
)(5700
105100
10898.2
10
3
K
b
T
m
?
?
?
?? ?
?
?
484
)(0 )5 7 0 0(1067.5 ????
?TM
T ?
27 /1000.6 mw??
Solve,
4) Planck?s Quantum Supposition普朗克量子假说
Planck?s Radiation Formula 普朗克辐射公式
a number of capable physicists advanced
theories based on classical physics,which,however,
had only limited success,
Example, 1896,Wien?s formula ( 维恩公式 )
T
c
T e
c
M ??
?
2
5
1
)(0
?
?
Where C1 and C2 are constants that must be
determined by the experimental data,
Wien?s formula isn?t fit to
the experimental points
at long wavelength,
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
)(0 TM ?
?(nm)
)
.(
1
1
?
?
m
cmw
?
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
)(0 TM ?
?(nm)
)
.(
1
1
?
?
m
cmw
?
Example:Rayleigh-jean?s formula瑞利 --金斯公式
1900年瑞利 --金斯利用经典电动力学和统计力学
（将固体当作谐振子且能量按自由度均分原则及
电磁辐射理论）得到一个公式,
C为光速
K=1.380658?10-23J/K
波尔兹曼常数
Rayleigh-jean?s
Formula isn?t fit the
experimental points
at short wavelength,
这通常称为“紫外灾难”
热辐射
实 验
4)(0
2
?
?
?
CKT
M T ?
1
1
2 52)(0
?
? ?
Tk
hCT
e
hCM
?
? ??
Planck?s formula 普朗克公式
In 1900 Max Planck pointed out that if Wien?s formula
were modified in a simple way it would prove to fit the data
precisely,It is,
constant k,Boltzmann?s
1
1
2 52
?
? ?
kT
h
e
hC
?
??
h=6.63?10-34(j·s) is called Planck?s constant,
Planck?s formula fit the data precisely,
)(0 TM ?
?(n m)
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
)
.(
1
1
?
?
m
cmw
?
普朗克注意到在过去的理论中，把黑
体中的原子和分子都看成可以吸收 或
辐射电磁波的谐振子，且电磁波与谐
振子交换能量时可以以任一大小的分
额进行，（从 0到 ?大）。普朗克当时
大胆地放弃了这一概念，提出了能量
的吸收与辐射只能按不连续的一份一份能量进行。 1) The atoms that make up black-body walls behave
like tiny electromagnetic oscillators,An oscillators
can?t have any energy but only energies given by
?nE n ?
?? h?
?3.2.1?n
sjh ??? ? 341063.6? is the oscillator frequency and h is a constant,
Planck?s Quantum Supposition,
where n is a quantum number,
but only in,jumps”,or quanta,These quanta of
energy are emitted when an oscillator changes
from one to another of its quantized energy states,
Thus,if changes by one unit,an amount of energy
given by
2) The oscillators don?t radiate energy continuously,
ΔE = Δnhv = hv
is radiated,
普朗克这一思想是完全背离经典物理的，并受
到当时许多人的怀疑和反对，包括当时的物理学
泰斗 ---洛仑兹。乃至当时普朗克自已也想以某种
方式来消除 ?nhE
n ?
这一关系式。它写道,
In his words,“My futile attempts to fit the
elementary quant of action (that is,the quantity h)
?
somehow into the classical theory continued for a
number of years,and they cost me a great deal of
effort.”
On the basis of his two assumptions,Planck
was able to derive his radiation law entirely from
theory,receiving a Nobel prize for this accom-
plishment in 1918,
普朗克用他自己的两个假设，就能够完全根据
理论来导出他的辐射定律。他由于这个成就，在
1918年荣获了诺贝耳奖金。
普朗克是量子论的奠基人。量子论和相对论构
成了近代物理学的研究基础。
1
1
2 52)(0
?
? ?
Tk
hCT
e
hCM
?
? ??
Discuss,
a） when h?>>kT（ high frequency 高频段）
1??
Tk
hC
?
Tk
hC
T ehCM
?
? ??
??
? 52)(0 2
T
C
T e
c
M ??
?
2
5
1
)(0
?
?
Wien?s formula 维恩公式 khCc ?2
21 2 hcc ??Let,
1
1
2 52)(0
?
? ?
Tk
hCT
e
hCM
?
? ??
Discuss,
a） when h?>>kT（ high frequency 高频段）
1??
Tk
hC
?
Tk
hC
T ehCM
?
? ??
??
? 52)(0 2
T
C
T e
c
M ??
?
2
5
1
)(0
?
?
Wien?s formula 维恩公式 khCc ?2
21 2 hcc ??Let,
Exp,A mass- spring system has a frequency ?=0.5HZ and a
spring constant k=3.0N/m and is osci-
llating with an amplitude of 10cm,
energy,)(105.11.03
2
1
2
1 222 JKAE ???????
a quanta?s energy,
)(103.35.01063.6 3434 Jh ?? ?????? ??
If n changes by unity,the fractional change in energy,
32
2
34
102.2
105.1
103.3 ?
?
?
??
?
???
E
E
The quantum number is,
30
34
2
1045
103.3
105.1 ??
?
???
?
?
?h
EN
E )(105.1 2 J??
X
F?
宏观看
是连续的
E )(105.1 2 J??
宏观看
是连续的
Thus for large-scale oscillators
the quantum numbers are enor-
mous and the quantized nature
of the energy of the oscillations
will not be apparent,
The Correspondence Principle （对应原理）,
Quantum physics reduces to classical physics at
large quantum numbers,
在大量子数情形下量子物理应当简化成经典物理
（ 1929年波尔提出）。
Homework,
量子物理
（ Quantum Physics）
2） 1990年，“紫外灾难”；
1） 1887年,A.A.Michelson-E.W.Morley实验否
定了绝对参考系的存在；
光是电磁波还是微粒？
1,黑体辐射、普朗克量子假说
（ Black-body Radiation,Planck?s Quantum Supposition）
热辐射
实 验
3） 1896年，首次发现放射性现象。
1） Heat Radiation （ 热辐射）
Experiment shows,
火
炉
600度 1000度 400度 Radiation relates to
temperature,
2） black body (黑体 )
black-body radiation (黑体辐射 )
抛光的铜镜表面吸收率,
一般金属表面吸收率,
煤烟吸收率,
02.0?总a
8.06.0 ??总a
98.095.0 ??总a Let us construct cavity in a metal block,through
the wall of which a small hole is drilled,This small
hole is called a black body,(a总 =1)
如远处不点灯的窗
若室内点灯
（是自身辐射）
a） spectral radiancy (单色辐出度 )
The quantity M(?T) is the rate at which energy is
radiated per unit time,per unit wavelength and
per unit area of surface for wavelengths lying in
the interval ? to ?+d? at the temperature T,
黑体
?
?
? d
dMM
T ?).(
).( 3?mWa总 =1
显然，它是波长和温度的函数
b) radiancy (辐出度 )
The appropriate quantity M(T) is the rate at which
energy is radiated per unit time and per unit area
of surface at the temperature T,
?dM
?d
黑体
).( 2?mW
a总 =1
显然，它是温度的函数,
b) radiancy (辐出度 )
单位时间内从物体单位面积上所辐射的各种
波长的总的辐射能，用 M（ T）表示。
TM
? ?? 0 ).()( ?? dMM TT
3) Studing black-body radiation experimentally
equipment 实验装置
A
L1
B P
L2 C
黑体
平行光管 三棱镜
测量系统
The law about black-body radiation黑体辐射规律
1.0 2.0 3.0 4.0 5.0
20
30
10
40
50
60
?(nm)
).( 11)(0 ?? mcmwM T ??
2200K
2000K
1800K
1600K
a) J.Stefan—Ludwig
Boltzmarn law,
4
)(0 TM T ??
mKw /1067.5 8????
J.Stefan—Ludwig
Boltzmarn constant
M0(T) depend only on the temperature and are
quite independent of the material and of the shape
and size of the cavity,
The law about black-body radiation
b)Wien displacement law
(维恩位移定律 ),
bT m ??
Kmb,108 9 8.2 3???
m?
,wavelength for
peak value
T,absolute temperature
火
炉
1000度 2000度 800度
炉火纯青
注意：以上两规律只适用于黑体，对非黑体只
近似成立。
1.0 2.0 3.0 4.0 5.0
20
30
10
40
50
60
?(nm)
).( 11)(0 ?? mcmwM T ??
2200K
2000K
1800K
1600K
Exp,The sun is a black-body,It?s wavelength fom
peak valueλm=5100A on the earth,Find the
surface temperature and radiancy,
例,太阳可以看成黑体，地球上测出其峰值波长
为 ?m=5100?，则其表面温度和辐出度为多少？
From
bT m ??
)(5700
105100
10898.2
10
3
K
b
T
m
?
?
?
?? ?
?
?
484
)(0 )5 7 0 0(1067.5 ????
?TM
T ?
27 /1000.6 mw??
Solve,
4) Planck?s Quantum Supposition普朗克量子假说
Planck?s Radiation Formula 普朗克辐射公式
a number of capable physicists advanced
theories based on classical physics,which,however,
had only limited success,
Example, 1896,Wien?s formula ( 维恩公式 )
T
c
T e
c
M ??
?
2
5
1
)(0
?
?
Where C1 and C2 are constants that must be
determined by the experimental data,
Wien?s formula isn?t fit to
the experimental points
at long wavelength,
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
)(0 TM ?
?(nm)
)
.(
1
1
?
?
m
cmw
?
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
)(0 TM ?
?(nm)
)
.(
1
1
?
?
m
cmw
?
Example:Rayleigh-jean?s formula瑞利 --金斯公式
1900年瑞利 --金斯利用经典电动力学和统计力学
（将固体当作谐振子且能量按自由度均分原则及
电磁辐射理论）得到一个公式,
C为光速
K=1.380658?10-23J/K
波尔兹曼常数
Rayleigh-jean?s
Formula isn?t fit the
experimental points
at short wavelength,
这通常称为“紫外灾难”
热辐射
实 验
4)(0
2
?
?
?
CKT
M T ?
1
1
2 52)(0
?
? ?
Tk
hCT
e
hCM
?
? ??
Planck?s formula 普朗克公式
In 1900 Max Planck pointed out that if Wien?s formula
were modified in a simple way it would prove to fit the data
precisely,It is,
constant k,Boltzmann?s
1
1
2 52
?
? ?
kT
h
e
hC
?
??
h=6.63?10-34(j·s) is called Planck?s constant,
Planck?s formula fit the data precisely,
)(0 TM ?
?(n m)
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
)
.(
1
1
?
?
m
cmw
?
普朗克注意到在过去的理论中，把黑
体中的原子和分子都看成可以吸收 或
辐射电磁波的谐振子，且电磁波与谐
振子交换能量时可以以任一大小的分
额进行，（从 0到 ?大）。普朗克当时
大胆地放弃了这一概念，提出了能量
的吸收与辐射只能按不连续的一份一份能量进行。 1) The atoms that make up black-body walls behave
like tiny electromagnetic oscillators,An oscillators
can?t have any energy but only energies given by
?nE n ?
?? h?
?3.2.1?n
sjh ??? ? 341063.6? is the oscillator frequency and h is a constant,
Planck?s Quantum Supposition,
where n is a quantum number,
but only in,jumps”,or quanta,These quanta of
energy are emitted when an oscillator changes
from one to another of its quantized energy states,
Thus,if changes by one unit,an amount of energy
given by
2) The oscillators don?t radiate energy continuously,
ΔE = Δnhv = hv
is radiated,
普朗克这一思想是完全背离经典物理的，并受
到当时许多人的怀疑和反对，包括当时的物理学
泰斗 ---洛仑兹。乃至当时普朗克自已也想以某种
方式来消除 ?nhE
n ?
这一关系式。它写道,
In his words,“My futile attempts to fit the
elementary quant of action (that is,the quantity h)
?
somehow into the classical theory continued for a
number of years,and they cost me a great deal of
effort.”
On the basis of his two assumptions,Planck
was able to derive his radiation law entirely from
theory,receiving a Nobel prize for this accom-
plishment in 1918,
普朗克用他自己的两个假设，就能够完全根据
理论来导出他的辐射定律。他由于这个成就，在
1918年荣获了诺贝耳奖金。
普朗克是量子论的奠基人。量子论和相对论构
成了近代物理学的研究基础。
1
1
2 52)(0
?
? ?
Tk
hCT
e
hCM
?
? ??
Discuss,
a） when h?>>kT（ high frequency 高频段）
1??
Tk
hC
?
Tk
hC
T ehCM
?
? ??
??
? 52)(0 2
T
C
T e
c
M ??
?
2
5
1
)(0
?
?
Wien?s formula 维恩公式 khCc ?2
21 2 hcc ??Let,
1
1
2 52)(0
?
? ?
Tk
hCT
e
hCM
?
? ??
Discuss,
a） when h?>>kT（ high frequency 高频段）
1??
Tk
hC
?
Tk
hC
T ehCM
?
? ??
??
? 52)(0 2
T
C
T e
c
M ??
?
2
5
1
)(0
?
?
Wien?s formula 维恩公式 khCc ?2
21 2 hcc ??Let,
Exp,A mass- spring system has a frequency ?=0.5HZ and a
spring constant k=3.0N/m and is osci-
llating with an amplitude of 10cm,
energy,)(105.11.03
2
1
2
1 222 JKAE ???????
a quanta?s energy,
)(103.35.01063.6 3434 Jh ?? ?????? ??
If n changes by unity,the fractional change in energy,
32
2
34
102.2
105.1
103.3 ?
?
?
??
?
???
E
E
The quantum number is,
30
34
2
1045
103.3
105.1 ??
?
???
?
?
?h
EN
E )(105.1 2 J??
X
F?
宏观看
是连续的
E )(105.1 2 J??
宏观看
是连续的
Thus for large-scale oscillators
the quantum numbers are enor-
mous and the quantized nature
of the energy of the oscillations
will not be apparent,
The Correspondence Principle （对应原理）,
Quantum physics reduces to classical physics at
large quantum numbers,
在大量子数情形下量子物理应当简化成经典物理
（ 1929年波尔提出）。
Homework,
