Transcript 量子力學發展史

量子力學發展史
近代科學發展之三
物理模型
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粒子模型
•
Allowed us to ignore unnecessary details of an object
when studying its behavior
系統與剛體
•
Extension of particle model
波動模型
兩種新模型
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量子粒子
邊界條件下的量子粒子
黑體幅射
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物體在任何溫度下皆會發出熱幅射(電磁
幅射)
電磁幅射波長會隨物體表面溫度的變化
而改變
黑體為一理想系統會吸收所有射入的幅射
由黑體發射出的電磁幅射稱為幅射
黑體近似
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黑體模型可近似為開
了一小孔洞的金屬空
腔
離開空腔的電磁幅射
其性質將只與空腔的
表面溫度有關
黑體實驗結論
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幅射的總功率與溫度的關係滿足Stefan定律
• Stefan’s Law
• P = s A e T4
• For a blackbody, e = 1
 s is the Stefan-Boltzmann constant
s = 5.670 x 10-8 W / m2 . K4
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波長分佈曲線的峰值位置隨溫度升高兒而往短
波長方向偏移，Wien位移定律
• Wien’s displacement law
 lmax T = 2.898 x 10-3 m.K
黑體幅射強度隨波長的分佈
l
l
幅射強度隨溫度升高
而增強
總幅射量隨溫度升高
而變大
• The area under the
curve
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峰值對應的波長隨
溫度升高而變短
紫外危機
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古典物理的預測與實驗
在短波處的結果發生極
大的差異
此現象稱為紫外危機，
尤其古典物理預測當幅
射波的波長趨近於零時
更會得到無限大的能量，
此與實驗觀察完全相反
Max Planck(拯救紫外危機的英雄)
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1858 – 1947
He introduced the
concept of “quantum
of action”
In 1918 he was
awarded the Nobel
Prize for the
discovery of the
quantized nature of
energy
Planck’s Theory of
Blackbody Radiation
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In 1900, Planck developed a structural model
for blackbody radiation that leads to an
equation in agreement with the experimental
results
He assumed the cavity radiation came from
atomic oscillations in the cavity walls
Planck made two assumptions about the
nature of the oscillators in the cavity walls
Planck’s Theory of
Blackbody Radiation
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In 1900, Planck developed a structural model
for blackbody radiation that leads to an
equation in agreement with the experimental
results
He assumed the cavity radiation came from
atomic oscillations in the cavity walls
Planck made two assumptions about the
nature of the oscillators in the cavity walls
Planck’s Assumption, 1
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The energy of an oscillator can have only
certain discrete values En
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En = n h ƒ
• n is a positive integer called the quantum number
• h is Planck’s constant
• ƒ is the frequency of oscillation
This says the energy is quantized
Each discrete energy value corresponds to a different
quantum state
Planck’s Assumption, 2
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The oscillators emit or absorb energy only in
discrete units
They do this when making a transition from
one quantum state to another
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The entire energy difference between the initial and
final states in the transition is emitted or absorbed as a
single quantum of radiation
An oscillator emits or absorbs energy only when it
changes quantum states
Energy-Level Diagram
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An energy-level
diagram shows the
quantized energy levels
and allowed transitions
Energy is on the vertical
axis
Horizontal lines
represent the allowed
energy levels
The double-headed
arrows indicate allowed
transitions
Correspondence Principle
(對應原理)
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當量子系統的量子態總數變大時，量子現象應
當會連續地轉變成古典現象
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Quantum effects are not seen on an everyday basis
since the energy change is too small a fraction of the
total energy
Quantum effects are important and become
measurable only on the submicroscopic level of atoms
and molecules
Photoelectric Effect
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The photoelectric effect occurs when
light incident on certain metallic surfaces
causes electrons to be emitted from
those surfaces
• The emitted electrons are called
photoelectrons
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The effect was first discovered by Hertz
Photoelectric Effect Apparatus
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When the tube is kept in
the dark, the ammeter
reads zero
When plate E is
illuminated by light having
an appropriate wavelength,
a current is detected by
the ammeter
The current arises from
photoelectrons emitted
from the negative plate (E)
and collected at the
positive plate (C)
Photoelectric Effect, Results
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At large values of DV, the
current reaches a
maximum value
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All the electrons emitted
at E are collected at C
The maximum current
increases as the intensity
of the incident light
increases
When DV is negative, the
current drops
When DV is equal to or
more negative than DVs,
the current is zero
Photoelectric Effect Feature 1
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Dependence of photoelectron kinetic energy
on light intensity
•
Classical Prediction
• Electrons should absorb energy continually from the
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electromagnetic waves
As the light intensity incident on the metal is increased,
the electrons should be ejected with more kinetic energy
Experimental Result
• The maximum kinetic energy is independent of light
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intensity
The current goes to zero at the same negative voltage
for all intensity curves
Photoelectric Effect Feature 2
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Time interval between incidence of light and
ejection of photoelectrons
•
Classical Prediction
• For very weak light, a measurable time interval should
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pass between the instant the light is turned on and the
time an electron is ejected from the metal
This time interval is required for the electron to absorb
the incident radiation before it acquires enough energy
to escape from the metal
Experimental Result
• Electrons are emitted almost instantaneously, even at
•
very low light intensities
Less than 10-9 s
Photoelectric Effect Feature 3
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Dependence of ejection of electrons on light
frequency
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Classical Prediction
• Electrons should be ejected at any frequency as long as
the light intensity is high enough
Experimental Result
• No electrons are emitted if the incident light falls below
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some cutoff frequency, ƒc
The cutoff frequency is characteristic of the material
being illuminated
No electrons are ejected below the cutoff frequency
regardless of intensity
Photoelectric Effect Feature 4
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Dependence of photoelectron kinetic energy
on light frequency
•
Classical Prediction
• There should be no relationship between the frequency
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of the light and the electric kinetic energy
The kinetic energy should be related to the intensity of
the light
Experimental Result
• The maximum kinetic energy of the photoelectrons
increases with increasing light frequency
Photoelectric Effect
Features, Summary
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The experimental results contradict all four
classical predictions
Einstein extended Planck’s concept of
quantization to electromagnetic waves
All electromagnetic radiation can be
considered a stream of quanta, now called
photons
A photon of incident light gives all its energy hƒ
to a single electron in the metal
Photoelectric Effect,
Work Function
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Electrons ejected from the surface of the metal
and not making collisions with other metal
atoms before escaping possess the maximum
kinetic energy Kmax
Kmax = hƒ – f
 f is called the work function
• The work function represents the minimum energy
with which an electron is bound in the metal
Some Work Function Values
Photon Model Explanation of the
Photoelectric Effect
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Dependence of photoelectron kinetic energy
on light intensity
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Kmax is independent of light intensity
K depends on the light frequency and the work
function
The intensity will change the number of photoelectrons
being emitted, but not the energy of an individual
electron
Time interval between incidence of light and
ejection of the photoelectron
•
Each photon can have enough energy to eject an
electron immediately
Photon Model Explanation of the
Photoelectric Effect, cont
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Dependence of ejection of electrons on
light frequency
• There is a failure to observe photoelectric
•
effect below a certain cutoff frequency, which
indicates the photon must have more energy
than the work function in order to eject an
electron
Without enough energy, an electron cannot be
ejected, regardless of the light intensity
Photon Model Explanation of the
Photoelectric Effect, final
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Dependence of photoelectron kinetic
energy on light frequency
• Since Kmax = hƒ – f
• As the frequency increases, the kinetic energy
will increase
• Once the energy of the work function is exceeded
• There is a linear relationship between the
kinetic energy and the frequency
Cutoff Frequency
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The lines show the linear
relationship between K and
ƒ
The slope of each line is h
The absolute value of the yintercept is the work
function
The x-intercept is the cutoff
frequency
•
This is the frequency below
which no photoelectrons are
emitted
Cutoff Frequency
and Wavelength
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The cutoff frequency is related to the work
function through ƒc = f / h
The cutoff frequency corresponds to a cutoff
wavelength
c
hc
lc 

ƒc
f
Wavelengths greater than lc incident on a
material having a work function f do not result
in the emission of photoelectrons
Applications of the
Photoelectric Effect
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Detector in the light meter of a camera
Phototube
• Used in burglar alarms and soundtrack of
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motion picture films
Largely replaced by semiconductor devices
Photomultiplier tubes
• Used in nuclear detectors and astronomy
Arthur Holly Compton
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1892 - 1962
Director at the lab of
the University of
Chicago
Discovered the
Compton Effect
Shared the Nobel
Prize in 1927
The Compton Effect,
Introduction
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Compton and coworkers dealt with Einstein’s
idea of photon momentum
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Einstein proposed a photon with energy E carries a
momentum of E/c = hƒ / c
Compton and others accumulated evidence of
the inadequacy of the classical wave theory
The classical wave theory of light failed to
explain the scattering of x-rays from electrons
Compton Effect,
Classical Predictions
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According to the classical theory,
electromagnetic waves of frequency ƒo incident
on electrons should
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Accelerate in the direction of propagation of the x-rays
by radiation pressure
Oscillate at the apparent frequency of the radiation
since the oscillating electric field should set the
electrons in motion
Overall, the scattered wave frequency at a
given angle should be a distribution of Dopplershifted values
Compton Effect, Observations
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Compton’s
experiments showed
that, at any given
angle, only one
frequency of
radiation is observed
Compton Effect, Explanation
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The results could be explained by treating the
photons as point-like particles having energy
hƒ and momentum hƒ / c
Assume the energy and momentum of the
isolated system of the colliding photon-electron
are conserved
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Adopted a particle model for a well-known wave
This scattering phenomena is known as the
Compton Effect
Compton Shift Equation
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The graphs show the scattered
x-ray for various angles
The shifted peak, l', is caused
by the scattering of free
electrons
•
h
l 'islcalled
 cos  shift
1Compton
o 
This
the
mec
equation
Compton Wavelength
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The unshifted wavelength, lo, is caused
by x-rays scattered from the electrons
that are tightly bound to the target atoms
The shifted peak, l', is caused by x-rays
scattered from free electrons in the
target
The Compton wavelength is
h
 0.00243 nm
me c
Photons and Waves Revisited
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Some experiments are best explained by the
photon model
Some are best explained by the wave model
We must accept both models and admit that
the true nature of light is not describable in
terms of any single classical model
Light has a dual nature in that it exhibits both
wave and particle characteristics
The particle model and the wave model of light
complement each other
Louis de Broglie
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1892 – 1987
Originally studied
history
Was awarded the
Nobel Prize in 1929
for his prediction of
the wave nature of
electrons
Wave Properties of Particles
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Louis de Broglie postulated that because
photons have both wave and particle
characteristics, perhaps all forms of
matter have both properties
The de Broglie wavelength of a particle
is
h
h
l 
p mv
Frequency of a Particle
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In an analogy with photons, de Broglie
postulated that particles would also have a
frequency associated with them
E
ƒ
h
These equations present the dual nature of
matter
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particle nature, m and v
wave nature, l and ƒ
Davisson-Germer Experiment
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If particles have a wave nature, then
under the correct conditions, they should
exhibit diffraction effects
Davission and Germer measured the
wavelength of electrons
This provided experimental confirmation
of the matter waves proposed by de
Broglie
Electron Microscope
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The electron microscope
depends on the wave
characteristics of electrons
The electron microscope has a
high resolving power because
it has a very short wavelength
Typically, the wavelengths of
the electrons are about 100
times shorter than that of
visible light
Quantum Particle
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The quantum particle is a new
simplification model that is a result of the
recognition of the dual nature of light and
of material particles
In this model, entities have both particle
and wave characteristics
We much choose one appropriate
behavior in order to understand a
particular phenomenon
Ideal Particle vs. Ideal Wave
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An ideal particle has zero size
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An ideal wave has a single frequency
and is infinitely long
• Therefore, it is localized in space
• Therefore, it is unlocalized in space
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A localized entity can be built from
infinitely long waves
Particle as a Wave Packet
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Multiple waves are superimposed so that one
of its crests is at x = 0
The result is that all the waves add
constructively at x = 0
There is destructive interference at every point
except x = 0
The small region of constructive interference is
called a wave packet
•
The wave packet can be identified as a particle
Wave Envelope
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The blue line represents the envelope function
This envelope can travel through space with a
different speed than the individual waves
Speeds Associated
with Wave Packet
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The phase speed of a wave in a wave
packet is given by
v phase  
• This is the rate of advance of a crest on a
k
single wave
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The group speed is given by
v g  d
dk of the wave packet itself
• This is the speed
Speeds, cont
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The group speed can also be expressed
in terms of energy and momentum
dE d  p2 
1
vg 

 2p   u


dp dp  2m  2m

This indicates that the group speed of
the wave packet is identical to the speed
of the particle that it is modeled to
represent
Electron Diffraction, Set-Up
Electron Diffraction, Experiment
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Parallel beams of mono-energetic
electrons are incident on a double slit
The slit widths are small compared to the
electron wavelength
An electron detector is positioned far
from the slits at a distance much greater
than the slit separation
Electron Diffraction, cont
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If the detector collects
electrons for a long enough
time, a typical wave
interference pattern is
produced
This is distinct evidence that
electrons are interfering, a
wave-like behavior
The interference pattern
becomes clearer as the
number of electrons reaching
the screen increases
Electron Diffraction, Equations
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A minimum occurs when
d sin 
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l
2
or
h
sin   
2 px d
This shows the dual nature of the electron
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The electrons are detected as particles at a localized
spot at some instant of time
The probability of arrival at that spot is determined by
finding the intensity of two interfering waves
Electron Diffraction,
Closed Slits
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If one slit is closed, the
maximum is centered
around the opening
Closing the other slit
produces another
maximum centered
around that opening
The total effect is the
blue line
It is completely different
from the interference
pattern (brown curve)
Electron Diffraction Explained
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An electron interacts with both slits
simultaneously
If an attempt is made to determine
experimentally which slit the electron goes
through, the act of measuring destroys the
interference pattern
•
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It is impossible to determine which slit the electron
goes through
In effect, the electron goes through both slits
•
The wave components of the electron are present at
both slits at the same time
Werner Heisenberg
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1901 – 1976
Developed matrix
mechanics
Many contributions
include
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Uncertainty Principle
•
Rec’d Nobel Prize in
1932
Prediction of two forms
of molecular hydrogen
Theoretical models of
the nucleus
The Uncertainty
Principle, Introduction
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In classical mechanics, it is possible, in
principle, to make measurements with
arbitrarily small uncertainty
Quantum theory predicts that it is
fundamentally impossible to make
simultaneous measurements of a
particle’s position and momentum with
infinite accuracy
Heisenberg Uncertainty
Principle, Statement

The Heisenberg Uncertainty Principle
states if a measurement of the position
of a particle is made with uncertainty Dx
and a simultaneous measurement of its
x component of momentum is made with
uncertainty Dp, the product of the two
uncertainties can never be smaller than

DxDp x 
2
Heisenberg Uncertainty
Principle, Explained
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It is physically impossible to measure
simultaneously the exact position and
exact momentum of a particle
The inescapable uncertainties do not
arise from imperfections in practical
measuring instruments
The uncertainties arise from the
quantum structure of matter
Heisenberg Uncertainty
Principle, Another Form
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Another form of the Uncertainty Principle
can be expressed in terms of energy and
time

DEDt 
2
This suggests that energy conservation
can appear to be violated by an amount
DE as long as it is only for a short time
interval Dt
Probability –
A Particle Interpretation

From the particle point of view, the
probability per unit volume of finding a
photon in a given region of space at an
instant of time is proportional to the
number N of photons per unit volume at
that time and to the intensity
Probability N
 I
V
V
Probability –
A Wave Interpretation

From the point of view of a wave, the
intensity of electromagnetic radiation is
proportional to the square of the electric
field amplitude, E
I E

2
Combining the points of view gives
Probability
 E2
V
Probability –
Interpretation Summary

For electromagnetic radiation, the probability
per unit volume of finding a particle associated
with this radiation is proportional to the square
of the amplitude of the associated em wave
•
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The particle is the photon
The amplitude of the wave associated with the
particle is called the probability amplitude or
the wave function
•
The symbol is Y
Wave Function
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The complete wave function Y for a
system depends on the positions of all
the particles in the system and on time
• The function can be written as
Y(r1, r2, … rj…., t) = y(rj)e-it
• rj is the position of the jth particle in the system
 = 2 p ƒ is the angular frequency
•
i  1
Wave Function, con’t
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The wave function is often complex-valued
The absolute square |y|2 = y*y is always real
and positive
 y* is the complete conjugate of y
• It is proportional to the probability per unit volume of
finding a particle at a given point at some instant

The wave function contains within it all the
information that can be known about the
particle
Wave Function,
General Comments, Final


The probabilistic interpretation of the
wave function was first suggested by
Max Born
Erwin Schrödinger proposed a wave
equation that describes the manner in
which the wave function changes in
space and time
•
This Schrödinger Wave Equation represents a key
element in quantum mechanics
Wave Function
of a Free Particle

The wave function of a free particle moving
along the x-axis can be written as y(x) = Aeikx
•
•

k = 2 p / l is the angular wave number of the wave
representing the particle
A is the constant amplitude
If y represents a single particle, |y|2 is the
relative probability per unit volume that the
particle will be found at any given point in the
volume
•
|y|2 is called the probability density
Wave Function
of a Free Particle, Cont
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
In general, the probability
of finding the particle in a
volume dV is |y|2 dV
With one-dimensional
analysis, this becomes
|y|2 dx
The probability of finding
the particle in the arbitrary
interval axb is
Pab  a y 2 dx
b
and is the area under the
curve
Wave Function
of a Free Particle, Final

Because the particle must be
somewhere along the x axis, the sum of
all the probabilities over all values of x
must be 1

Pab   y dx  1
2
• Any wave function satisfying this equation is
•
said to be normalized
Normalization is simply a statement that the
particle exists at some point in space
Expectation Values

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
y is not a measurable quantity
Measurable quantities of a particle can
be derived from y
The average position is called the
expectation value of x and is defined as

x   y * xydx
Expectation Values, cont

The expectation value of any function of
x can also be found
f x    y * f x ydx

• The expectation values are analogous to
averages
Particle in a Box

A particle is confined to a
one-dimensional region of
space
•


The “box” is onedimensional
The particle is bouncing
elastically back and forth
between two impenetrable
walls separated by L
Classically, the particle’s
momentum and kinetic
energy remain constant
Wave Function
for the Particle in a Box

Since the walls are impenetrable, there
is zero probability of finding the particle
outside the box
y(x) = 0 for x < 0 and x > L

The wave function must also be 0 at the
walls
• The function must be continuous
y(0) = 0 and y(L) = 0
Potential Energy
for a Particle in a Box

As long as the particle is
inside the box, the
potential energy does
not depend on its
location
•

We can choose this
energy value to be zero
The energy is infinitely
large if the particle is
outside the box
•
This ensures that the
wave function is zero
outside the box
Wave Function of a Particle
in a Box – Mathematical

The wave function can be expressed as
a real, sinusoidal function
 2p x 
y ( x )  A sin 

 l 

Applying the boundary conditions and
using the de Broglie wavelength
 np x 
y ( x )  A sin 

 L 
Graphical Representations
for a Particle in a Box
Wave Function of the
Particle in a Box, cont




Only certain wavelengths for the particle
are allowed
|y|2 is zero at the boundaries
|y|2 is zero at other locations as well,
depending on the values of n
The number of zero points increases by
one each time the quantum number
increases by one
Momentum of the
Particle in a Box


Remember the wavelengths are
restricted to specific values
Therefore, the momentum values are
also restricted
h
nh
p 
l 2L
Energy of a Particle in a Box


We chose the potential energy of the
particle to be zero inside the box
Therefore, the energy of the particle is
just its kinetic energy
 h2  2
En  
n
2 
 8mL 

n  1, 2, 3
The energy of the particle is quantized
Energy Level Diagram – Particle
in a Box
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
The lowest allowed energy
corresponds to the ground
state
En = n2E1 are called excited
states
E = 0 is not an allowed state
The particle can never be at
rest
The lowest energy the
particle can have, E = 1, is
called the zero-point
energy
Boundary Conditions



Boundary conditions are applied to determine
the allowed states of the system
In the model of a particle under boundary
conditions, an interaction of a particle with its
environment represents one or more boundary
conditions and, if the interaction restricts the
particle to a finite region of space, results in
quantization of the energy of the system
In general, boundary conditions are related to
the coordinates describing the problem
Erwin Schrödinger

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1887 – 1961
Best known as one of
the creators of quantum
mechanics
His approach was shown
to be equivalent to
Heisenberg’s
Also worked with
•
•
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statistical mechanics
color vision
general relativity
Schrödinger Equation

The Schrödinger equation as it applies to
a particle of mass m confined to moving
along the x axis and interacting with its
environment through a potential energy
function U(x) is
h 2 d 2y

 Uy  Ey
2
2m dx

This is called the time-independent
Schrödinger equation
Schrödinger Equation, cont
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Both for a free particle and a particle in a
box, the first term in the Schrödinger
equation reduces to the kinetic energy of
the particle multiplied by the wave
function
Solutions to the Schrödinger equation in
different regions must join smoothly at
the boundaries
Schrödinger Equation, final
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y(x) must be continuous
y(x) must approach zero as x
approaches ±
• This is needed so that y(x) obeys the
normalization condition

dy / dx must also be continuous for finite
values of the potential energy
Solutions of the
Schrödinger Equation

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Solutions of the Schrödinger equation may be
very difficult
The Schrödinger equation has been extremely
successful in explaining the behavior of atomic
and nuclear systems
•
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Classical physics failed to explain this behavior
When quantum mechanics is applied to
macroscopic objects, the results agree with
classical physics
Potential Wells
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A potential well is a graphical
representation of energy
The well is the upward-facing region of
the curve in a potential energy diagram
The particle in a box is sometimes said
to be in a square well
• Due to the shape of the potential energy
diagram
Schrödinger Equation
Applied to a Particle in a Box

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In the region 0 < x < L, where U = 0, the
Schrödinger equation can be expressed in the
form
d 2y
2mE
2


y


k
y
2
2
dx
The most general solution to the equation is
y(x) = A sin kx + B cos kx
•
A and B are constants determined by the boundary
and normalization conditions
Schrödinger Equation Applied to
a Particle in a Box, cont.

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Solving for the allowed energies gives
 h2  2
En  
n
2 
 8mL 
The allowed wave functions are given by
•
•
2
 np x 
 np x 
y ( x )  A sin 

sin 


L
L
L




The second expression is the normalized wave
function
These match the original results for the particle in a
box
Application – Nanotechnology
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Nanotechnology refers to the design and
application of devices having dimensions
ranging from 1 to 100 nm
Nanotechnology uses the idea of trapping
particles in potential wells
One area of nanotechnology of interest to
researchers is the quantum dot
•
•
A quantum dot is a small region that is grown in a
silicon crystal that acts as a potential well
Storage of binary information using quantum dots is
being researched
Quantum Corral
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Corrals and other
structures are used
to confine surface
electron waves
This corral is a ring
of 48 iron atoms on a
copper surface
The ring has a
diameter of 143 nm
Tunneling
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The potential energy
has a constant value
U in the region of
width L and zero in
all other regions
This a called a
square barrier
U is the called the
barrier height
Tunneling, cont
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Classically, the particle is reflected by the
barrier
•
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Regions II and III would be forbidden
According to quantum mechanics, all regions
are accessible to the particle
•
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The probability of the particle being in a classically
forbidden region is low, but not zero
According to the Uncertainty Principle, the particle can
be inside the barrier as long as the time interval is
short and consistent with the Principle
Tunneling, final
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The curve in the diagram represents a full
solution to the Schrödinger equation
Movement of the particle to the far side of the
barrier is called tunneling or barrier
penetration
The probability of tunneling can be described
with a transmission coefficient, T, and a
reflection coefficient, R
Tunneling Coefficients
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The transmission coefficient represents the
probability that the particle penetrates to the
other side of the barrier
The reflection coefficient represents the
probability that the particle is reflected by the
barrier
T+R=1
•
•
The particle must be either transmitted or reflected
T  e-2CL and can be non zero
Tunneling is observed and provides evidence
of the principles of quantum mechanics
Applications of Tunneling

Alpha decay
• In order for the alpha particle to escape from
the nucleus, it must penetrate a barrier whose
energy is several times greater than the
energy of the nucleus-alpha particle system
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Nuclear fusion
• Protons can tunnel through the barrier caused
by their mutual electrostatic repulsion
More Applications of Tunneling –
Scanning Tunneling Microscope
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An electrically conducting probe with a very
sharp edge is brought near the surface to be
studied
The empty space between the tip and the
surface represents the “barrier”
The tip and the surface are two walls of the
“potential well”
The vertical motion of the probe follows the
contour of the specimen’s surface and
therefore an image of the surface is obtained
Cosmic Temperature

In the 1940’s, a structural model of the
universe was developed which predicted
the existence of thermal radiation from
the Big Bang
• The radiation would now have a wavelength
•
distribution consistent with a black body
The temperature would be a few kelvins
Cosmic Temperature, cont

In 1965 two workers at Bell Labs found a
consistent “noise” in the radiation they
were measuring
• They were detecting the background radiation
•
•
from the Big Bang
It was detected by their system regardless of
direction
It was consistent with a back body at about 3
K
Cosmic Temperature, Final
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Measurements at
many wavelengths
were needed
The brown curve is
the theoretical curve
The blue dots
represent
measurements from
COBE and Bell Labs