Download Lecture IV : Feb 8, 2016 Learning from Two Hole Experiment (A

Lecture IV : Feb 8, 2016
Learning from Two Hole Experiment
(A) Watch first Dr Quantum video
What to expect when
• Single Slit.. First Particle and then Waves ...
• Double Slit.. First Particles and then Waves
• What we see with electrons.... ( Wave like interference pattern)
• Close One slit...... ( Interference pattern disappears)
• Shoot single electron at a time..... ( Interference pattern survives)
• Try to observe which hole the electron passes by shining light... ( Interference pattern
disappears)
• Confirm the identity of what arrives at the screen.. do we see electron as a whole or
something else... ( Electron arrives as an electron on the screen)
(B) Watch Brian Greene’s Video
• What kind of wave the electron is : It is all Probability Wave.
• What is the relevant question we should be asking... Since we cannot see the electron, the
question like which slit the electron goes through is not the right question. The question we
should be asking is: what is the probability that the electron will go through slit 1 or slit 2.
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How to Distinguish Particles and Waves
(A) Particles
Come in lumps
N12 = N1 + N2 .... No interference ( Classical Behavior – seen with marbles, tennis balls etc.. )
where N1 is the number of particles coming from hole 1 when hole 2 is closed. N2 is the number
of particles coming from hole 2 , when hole 1 is closed. N12 is the number of particles on the
scree when both the slits or hole are open.
N1 , N2 and N12 can also be viewed as probability of particles arriving at the screen in the
three cases described above.
(B) Waves:
Does not come in lumps, we measure intensity
I12 6= I1 + I2 .... Interference ( Classical Behavior )
Interference can be explained by a simple equation . To see this, Define a new quantity called
amplitude ( or probability amplitude ), which we denote as A
I1 = A21
(1)
I2 = A22
(2)
I12 = A212 = (A1 + A2 )2 6= I1 + I2
(3)
(4)
A12 = A1 + A2
Note, unlike intensity, amplitudes of two waves when combined can cancel each other.
(C) Electrons or Photons
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(5)
Come in LUMPS... act like particles
Show interference, act like waves
N12 6= N1 + N2
In this sense electron acts like both waves and particles..
Analyze this; To understand this peculiar behavior. Which Hole does the Electron pass??
(a) Close one hole...
(b) Proposition I... Each electron goes through either one or two... False..
(c) Proposition I is false..
(d) Watch through which hole it goes through...., we find electron comes from hole 1 and 2
we can separate them as coming from 1 or 2.. That means N12 = N1 + N2 . In others words,
we get different answer when we turn out the light.
(e) This implies that light effects the motion of the electron... That is electrons unlike ball
are delicate, getting bounced off light..
(f) Make the light dim... .. We get fewer and fewer photons... Weak light means fewer
photon..... we see fewer and fewer electrons and we see interference
It turns out that it is IMPOSSIBLE to design any experiment where we can observe which
hole the electron goes and not to destroy the interference
Heisenberg uncertainly principle...
This is basic characteristic of nature.... This is true for all microscopic particles...
The behavior we see in other places is same... UNPREDICTABILITY
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This is how the nature is. Unpredictability is nothing to do with our inability...
This is why Brian Greene calls the electrons coming from “two-hole” experiments as
Probability Waves
Double slit or two hole experiment shows that electrons act both like particles as well as
waves.
SUMMARY
Three shocking facts about double slit with electrons:
(1) Interference pattern, just like waves..
(2) Interference disappears when one tries to see which hole the electron goes through
(3) At any given spot on the screen, the number of particles detected can only be described
by laws of probability
For particles, we usually ask questions like, what is their mass m, speed or velocity v and
momentum p = mv
For waves, we want to know the wave length λ, frequency f and speed c with which the
wave is propagating.
I.
WAVE OR PARTICLE, WHAT IS IT ???
Try telling someone that electron can sometimes act like a particle and sometimes like a
wave.. It is bound to cause confusion and skepticism.. When we think of particle, we think of
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tennis balls or a pebble and mention of waves takes us dreaming of beaches and oceans. Perhaps
the only relationship between particle and waves that we know of are the ripples generated in a
pond by tossing a pebble. Richard Feynman sums up the situation by saying that we do not know
what the electron is, but there is something simple about it, it is like a photon.
Quantum world is inhabited by species that have dual personality: they can behave either as a
particle or as a wave. These species are not some extra terrestrial objects. They can be base balls or
base ball players themselves as well as electrons, Higgs particle or quarks. Interestingly, they can
also be light waves or X-rays or waves in a violin string. This revolutionary idea of Wave-Particle
Duality was proposed by de Broglie in his PhD thesis in 1924 for which he was awarded Nobel
prize in 1929.
FIG. 1: de-Broglie wavelengths for matter waves : baseball, electrons in H-atom and Rubidium atoms at
low temperatures
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A.
Matter Waves
Consider a particle of mass m moving with a velocity v. Momentum of the particle is defined
as,
p = mv
(6)
Momentum is a measure of the impact in any collision.
In quantum world, particles are characterized by wave length and frequency, in addition to
usual particle-like characteristics such as mass, charge and velocity or momentum. These matter
waves, known as de Broglie waves reflect the wave particle duality of matter. According to the
de Broglie hypothesis, the wavelength associated with a particle is inversely proportional to its
momentum p while the frequency f of matter waves, is proportional to the total energy E of the
particle. The constant of proportionality is a new fundamental constant h, called the Planck’s
constant, named after Max Planck who discovered it in 1900 ( Nobel prize 1918). The following
two equations describe the de-Broglie hypothesis:
h
E
,
f=
(7)
p
h
In applications where it is natural to use the angular frequency ω = 2πf (i.e. where the
λ=
frequency is expressed in terms of radians per second instead of rotations per second or Hertz)
it is often useful to write expressions in terms of reduced Planck constant which is the Planck
constant divided by 2π, and is denoted as ~ (pronounced ”h-bar”):
h
= 1.054571726(47) · 10−34 Joule − sec
(8)
2π
The constant ~ is what lies at the heart of quantum science. Yes, it is a pretty small and
~=
that is why quantum effects are usually irrelevant in macroscopic world. Readers will notice the
presence of ~ explicitly in all equations providing quantum description of a particle.
Figure (1) shows de-Broglie wave calculations for different kinds of matter that includes
macroscopic objects at room temperature, electrons in an atom and an atom at very low
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temperature. Quantum effects become important when the de-Broglie wave length λ is of the
same order as the characteristic length scale in the system. This is the case for elections inside the
atom or for atoms at extremely low temperature. In other words, electrons inside an atom exhibits
wave-like properties. Similarly, an atom such as Rubidium, acts like a wave at temperatures of
the order of Nano kelvin.
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Some Constants
mass of the electron, me = 9X10−31 ≈ 10−30
That means we will need 1030 electrons to weigh one kg, which is thousand billion, billion,
billion.
mass of the proton, mp ≈ 2000 times the mass of electron
Planck constant h = 6.63X10−34 Joule − sec
One Calorie is 4.2 Joules
Unit of energy in diet is Kilo-Calorie
HOW TO CALCULATE de-Broglie wave length for photons
Photons have energy E and momentum p = E/c.
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B.
Establishing Wave Nature of Matter Waves
Young’s double slit interferometer ( two-hole setup) introduced about two hundred years ago,
is one of the most versatile tool to distinguish waves and particle Diffractions through crystals,
where atoms are arranged in a periodic pattern provide a multi-hole analog of the double-hole
set up. The de Broglie hypothesis, regarding wave nature of particles was confirmed three
years after de-Broglie’s prediction for electrons (which have a rest-mass) with the observation
of electron diffraction in two independent experiments. At the University of Aberdeen George
Paget Thomson passed a beam of electrons through a thin metal film and observed the predicted
interference patterns. At Bell Labs Clinton Joseph Davisson and Lester Halbert Germer guided
their beam through a crystalline grid. Thomson and Davisson shared the Nobel Prize for Physics
in 1937 for their work.
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QUIZ I : FEB 3, 2016... ANSWERS
(1) Size of the H-atom is 10−8 meters. Take H-atom. Magnify it 10 times. Repeat this process.
How many times you have to repeat this process so that the image is of the size of one centimeter
?? (ANS: 8 times)
(2) Write 100 billion in scientific notation ( ANS: 1011
(3) In classical physics, there are two main laws (N) Newton’s Laws of motion, (M) Maxwell’s
Equations
State whether (M) or (N) explain the following
(3.1) Sound waves (N)
(3.2) Water Waves (N)
(3.3) Light Waves (M)
(3.4) Motion of the Tennis balls (N)
(3.5) Electric and Magnetic phenomena (M)
(3.6) Motion of a runner (N)
(3.7) X-rays (M)
(4) “ Einstein’s theory of Relativity is a branch of Quantum Physics ”.. True or False. (
ANS: False)
(5)Write in order of increasing wavelength: Microwaves, X-rays,radio waves,red light,blue
light (ANS: X-rays, Microwaves, Blue, Red, Radio )
(6)Write in order of increasing frequency: Microwaves, X-rays, radio waves, red light, blue light
(ANS: Radio, Red, Blue, Microwaves, X-rays)
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