Lesson 5.6 - Wave-Particle Duality
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THE PHENOMENA THAT YOU WILL ENCOUNTER BEHAVE LIKE NOTHING YOU HAVE ENCOUNTERED IN YOUR DIRECT EXPERIENCE.
YOU WILL ENCOUNTER THINGS AT EXTREMELY SMALL SCALES
THEY DO NOT BEHAVE LIKE WAVES, PARTICLES, CLOUDS, BALLS, SPRINGS, OR ANYTHING ELSE YOU HAVE SEEN
IF YOU THINK YOU COMPLETELY UNDERSTAND IT, YOU HAVEN'T THOUGHT ABOUT IT ENOUGH
Imagine a gun. Not a very good gun: It fires bullets in a random angular spread. It is being fired at a wall of armour plating with two gaps in it, followed by another wall to catch the bullets.
What we are looking at is the probability of the arrival of individual 'lumps' of bullet and there in no interference between individual 'lumps'.
A bullet can either go through one hole or the other, but not both.
Now, there is no 'lumpiness'. Wave can reach the back wall with any intensity (height) and the waves can simultaneously go through both holes and interfere with each other (See Unit 4).
Now we use electrons.
This can be accomplished by heating a wire in a positively charged box with a hole in it. We now have an 'electron gun'.
It turns out that at high enough velocities and small enough holes (atoms in a crystal) the electrons will interfere and form an interference pattern.
TWO STRANGE CONCLUSIONS:
- Electron (and thus matter) must have some inherint wave-nature to create an interference pattern
- An electron must be able to simultaneously be in both holes and not by discrete objects.
Now if I change my apparatus so that I can "see" the electrons as they come through the holes, an even more bizarre thing happens:
The diffraction pattern disappears and we see the result from the bullet experiment.
HOW IS THIS POSSIBLE?We change what we are looking at and the whole situation changes.
- I look at the screen and I see diffraction (waves)
- I look at the holes and there is no diffraction (particles)
THE CENTRAL TENET OF QUANTUM MECHANICS
We call this the wave-particle duality of quantum mechanics.
How do we picture such a thing? We don't! It is impossible for visualize this in any appropriate matter. The only way we can truly understand this is through the mathematics of quantum mechanics.
WAIT A SEC!!!
An electron is a wave? Mater is a wave?
Let's look at the Compton momentum relationship.
\(p= \frac{h}{\lambda}\)
If we consider a particle with non-zero mass, we can also use the classical expression for its momentum \(p=mv\)
\(mv= \frac{h}{\lambda}\)
\( \lambda = \frac{h}{mv}\)
We call this wavelength the deBroglie Wavelength.
EXAMPLE PROBLEM #1
Determine the deBroglie wavelength of a 0.10kg ball travelling 20m/s.SOLUTION:
EXAMPLE PROBLEM #2
Determine the deBroglie wavelength of an electron with kinetic energy of 24eV.SOLUTION:
SUMMARY
- Both light and matter are governed by the same quantum mechanical framework
- They can both behave like a wave and a particle depending on how it is being observed
- The act of observing something must necessarily disturb it
- A photon has particle-like momentum \(p= \frac{h}{\lambda}\)
- Matter has a wave-like wavelength \( \lambda = \frac{h}{mv}\)