Wave-Particle Duality Notes
I wrote these notes for Science A-39, in Fall 1998, after watching
Richard Feynmann's lecture on the topic, which is available as a video,
probably, at the Cabot library. These notes go into a bit more detail
than you probably need in this course, but it's worth a look if you
are mystified by the wave-particle duality.
The essential point is that light behaves neither like a rain of particles,
nor purely like conventional waves (on water, for example). It appears
to sometimes be particle-like, and sometimes be wavelike, and it is often
useful to think of it using one or the other interpretation. However,
it is important to remember that light is actually something quite different
from either conventional particles or conventional waves.
The wavelike behaviour of light includes interference patterns and
diffraction effects. The particle-like behaviour is that when we
turn down the intensity of a light source enough, in stead of getting
a very faint constant signal, we get discrete lumps of light, called
"photons", that turn up at random intervals and only
in one place at a time. These photons always have
the same amount of energy in them for light of one colour.
The tricky thing though, is that the interference pattern that
you would work out from a conventional wave tells you where the
photon is most likely to be detected.
The discrete energy levels in atoms come from the fact that electrons
(those little charged things that orbit around the nucleus) also
have wave-like and particle-like properties, just like photons.
In fact, people have even done interference experiments with electrons,
and gotten completely analogous results to the ones discussed below.
For atoms, the wavelength depends on the the electron's energy,
and the energy of the electron depends on how far away it is from
the nucleus. The electron can only exist in places where there is
an even number of wavelengths around its orbit.
The last page is on the Heisenberg uncertainty principle in
quantum mechanics. YOU DO NOT HAVE TO KNOW THIS, but I'm putting
it in for those who are curious. I would love to enlarge on this
outside of section. Briefly, the uncertainty principle states
that you can't completely specify both the position and velocity
for one of these wave-particle objects. It really comes from
the wave-like properties.
When we discussed water waves in section,
I mentioned that waves passing through a very small opening spread
out in circular ripples on the other side. This is because on the
far side of the opening, the water only sees shaking at one location,
much like you would have if a stone dropped in right there.
If you widen the opening, the waves only occur in the "shadow"
of the opening, and don't spread out much to the sides.
For photons or electrons in a double-slit experiment, the position
uncertainty is just the size of the opening, since we don't know
exactly where it went through. The velocity uncertainty is related
to the spreading out of the wave pattern. If it is more spread out,
then the particle could turn up anywhere along a wide range of
positions on the detecting screen to the right. The "velocity"
(in the up/down direction on these pictures)
would then be whatever velocity was needed to get it from the opening
over to where it landed on the screen. If the opening is small,
very large velocities are possible, but if the opening is large,
the velocities will always be small.
