PHYS 117B.02 Lecture Apr 4

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PHYS 117B.02 Lecture Apr 4

• The last few lectures weve been switching gears
  from classical to quantum physics

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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 todays lecture is particles and
  waves.

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We already learned some things about particles
and waves

• Photoelectric effect light behaves as a
  particle but previously we have shown that it
  also behaves as a wave.
• Atomic spectra Bohrs 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 well talk about particle waves and quantum
  behavior in general
• One lucky break electrons behave just like
  light!
• Ill 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 2pr n l But, you
need to assume that the electron is a wave ! Now
if l h/p 2pr n h/( mv) gt L mvr n h/2p
Angular momentum is quantized L hn/2p,
n1,2,3 .
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Particles and waves de Broglies hypothesis (
1924)

• Nature is beautifully symmetric.
• If light behaves both as a particle and a wave,
  then matter ( electrons, protons, etc) should
  also have wave properties.
• l h/p , where h is Plancks 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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Lets analyze the distribution of bullets at the
backstop

• 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 Measure P1
Close slit 1 Measure P2
Both slits open Measure P P1 P2
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Do an experiment with water waves

• Now we measure intensity of the wave
• I E2
• I12 ? I1 I2
• Interference
• I12 I1 I2 2 v(I1I2) cos f

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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/twosl
  itsb.html

If you take PHYS225 you can do this experiment
yourself !
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Electrons produce an interference pattern!
bullets

• 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 ?

water
electrons
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Watching the electrons

• Lets 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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Lets be more sneaky

• Reduce the intensity of the light source
• or
• Change the wavelength

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Lets first reduce the intensity

• OK here we go
• Three groups of electrons
• A group that we see going through slit 1
• A group that we see going through slit 2
• A group that we dont see, but we detect with our
  detector
• And the result is
• Group 1 and 2 perfectly behaved (no interference)
• Group 3 produces an interference pattern!

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Lets now try to increase the wavelength

• 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
• 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 well get a
  fuzzy spot
• The interference pattern will reappear, but we
  will no longer be able to tell through which slit
  the electron went
• Heisenbergs uncertainty principle
• 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 ?
• ?E ?t ?

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Probability in classical and quantum physics

• Assume we have an ideal experiment
• 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 (dont 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