Transcript slides - Vanderbilt HEP

PHYS 117B.02 Lecture Apr 4
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The last few lectures we’ve been switching
gears from classical to quantum physics
This way: The quantum leap
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“If, in some cataclysm , all of scientific knowledge were to
be destroyed, and only one sentence passed on to the next
generation of creatures, what statement would contain the
most information in the fewest words ? I believe it is the
atomic hypothesis ( or the atomic fact) that all things are
made of atoms – little particles that move around in
perpetual motion, attracting each other when they are a
little distance apart, but repelling upon being squeezed
into one another.”
Richard Feynman
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To understand atoms we need to
understand the quantum behavior.
The theme of today’s lecture is particles
and waves.
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We already learned some things about
particles and waves:
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Photoelectric effect – light behaves as a particle … but previously
we have shown that it also behaves as a wave.
Atomic spectra : Bohr’s model explained many features of the
hydrogen atom spectra (and hydrogen-like atoms) by assuming
that angular momentum is quantized and that photons are
emitted and absorbed when electrons jump from one orbit to
another
Today we’ll talk about particle waves and quantum behavior in
general
One “lucky break” – electrons behave just like light!
I’ll mostly follow R. Feynman, but our textbook also has nice
discussion on the topic in ch 38.9 and ch 39.1-3
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The Bohr atom: another perspective
You can also think of the
quantization
of L as requiring the
electrons to form
standing waves along the
classical orbit:
Angular momentum is
quantized: L = hn/2p,
n=1,2,3 ….
2pr = n l
But, you need to assume that
the electron is a wave !
Now if l = h/p
2pr = n h/( mv)
=> L = mvr = n h/2p
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Particles and waves: de Broglie’s
hypothesis ( 1924)
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Nature is beautifully symmetric.
If light behaves both as a particle and a
wave, then matter ( electrons, protons, etc)
should also have wave properties.
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l = h/p , where h is Planck’s constant and p is the
momentum of the particle
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What is the wavelength of the electron ?
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Double slit experiment revisited: Shooting
solid objects (particles) through double slit
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Let’s analyze the distribution of bullets at
the backstop
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The assumptions:
 Machine gun shoots at constant rate
 Only whole bullets arrive at the
detector
 Move the detector and count how
many bullets are collected at each
position for some fixed amount of time
Define probability:
 P = N (x)/Ntotal
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The results of the bullets experiment
Close slit 2
Close slit 1
Measure P1
Measure P2
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Both slits open:
Measure P = P1 + P2
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Do an experiment with water waves
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Now we measure
intensity of the wave:
I ~ E2
I12 ≠ I1 + I2
Interference:
I12 = I1 + I2 + 2 √(I1I2) *cos φ
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But what will happen if our bullets are
microscopic particles ?
Two slit experiment using electron gun:
http://www.colorado.edu/physics/2000/applets/twoslitsb.html
If you take PHYS225 you can do
this experiment yourself !
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Electrons produce an interference pattern!
bullets
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water
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electrons
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Even if we shoot electrons
one-by-one - we get an
interference pattern !
Each electron interferes
with itself !
How can this be ?
How do the electrons pass
through the slits ?
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Watching the electrons
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Let’s try to observe through which slit the electron will go
Shine light near the slits: photons scattered from the electron will come to our
eyes – bingo ! We know which way the electron went!
Hmm… it looks like we are disturbing the electrons with the light!
Of course – we know that light has E and B field, carries energy, exerts
pressure !
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Let’s be more sneaky
Reduce the intensity of the light source
or
 Change the wavelength
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Let’s first reduce the intensity:
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OK here we go:
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Three groups of electrons
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A group that we see going through slit 1
A group that we see going through slit 2
A group that we don’t see, but we detect with our
detector
And the result is:
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Group 1 and 2 perfectly behaved (no interference)
Group 3 produces an interference pattern!
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Let’s now try to increase the wavelength
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Longer wavelength means smaller momentum: l = h/p , so we
will disturb the electrons less
Gradually change the photon wavelength ( make the light
“redder”
In the beginning – all looks the same. We can tell the position of
the electrons at the slits and there is no interference
Remember:
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in order to resolve the position of the electrons, the wavelength of
the photon has to be of the order of the distance between the slits
Once we get to longer wavelengths: we’ll get a fuzzy spot
The interference pattern will reappear, but we will no longer be able
to tell through which slit the electron went
Heisenberg’s uncertainty principle:
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It is impossible to design an experiment in which we can measure
which one of two possible paths was taken without destroying the
interference pattern!
∆px ∆x ≥ ћ
∆E ∆t ≥ ћ
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Probability in classical and quantum physics
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Assume we have an ideal experiment:
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We know the initial conditions (electron leaves the
gun headed to the slits)
There are no external influences
We can NOT predict the final state of the system
exactly (don’t know where it will land)
We can only predict the odds !
This is different from classical physics
We have given up the idea that the world is
deterministic
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