1. Wave-Particle Duality
SPH4U

2. You take the blue pill, the story ends, you wake up in your bed and believe whatever you want to believe. You take the red pill, you stay in Wonderland and I show you how deep the rabbit-hole goes.

3. Light is a Wave
Light exhibits wave behaviours: diffraction, interference, etc.

4. Light is a Particle
Light also exhibits particle behaviours: the photoelectric effect, Compton scattering, etc.

5. Light is Both
Conclusion: Light is both a wave and a particle and its behaviour depends on the situation.
Hi, I’m a wave.
Hi, I’m a particle.

6. Mind Blown
So light directed through a single slit will always produce a diffraction pattern of constructive and destructive interference

7. Mind Blown
So light directed through a single slit will always produce a diffraction pattern of constructive and destructive interference even if there is only one photon at a time in the apparatus.
Still a wave!

8. The Copenhagen Interpretation
In the apparatus, the photon exists in a superposition of all possible states, which can interfere with each other
Probability distribution of photon in here looks like interference pattern.

9. The Copenhagen Interpretation
In the apparatus, the photon exists in a superposition of all possible states, which can interfere with each other until the photon is observed (by the screen).
Result of many photons with that probability distribution.

10. The Copenhagen Interpretation
The act of observation collapses the wave function.

11. Schrodinger’s Cat
The photon is Schrodinger’s Cat. Schrodinger’s Cat is a thought experiment illustrating the difficulty of applying the Copenhagen Interpretation to everyday objects.

12. Schrodinger’s Cat
A cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal monitor detects a radioactive decay, the flask is shattered, releasing the poison that kills the cat.

13. Schrodinger’s Cat
While the box is closed, the cat is simultaneously both alive and dead. It is the act of opening the box that determines the state of the cat.

14. Application
In quantum computing, “qubits” are in a probabilistic superposition of possible states. Bits can be 0 or 1. Qubits can be 0 and 1. This allows a computer to perform multiple operations simultaneously.

15. Observation
That the act of observation changes a system limits what we can know about a system. For example, imagine we wanted to know the position of an electron by observing it with a photon

16. Observation
The photon would transfer some unknown quantity of its momentum to the electron.

17. Observation
The more accurately we try to locate the electron by using a smaller-wavelength (higher-momentum) photon, the less accurately we know the final momentum.

18. Heisenberg’s Uncertainty Principle
Heisenberg’s Uncertainty Principle states that if Dx is the uncertainty in a particle’s position and Dp is the uncertainty in its momentum,

19. Example
What is the uncertainty in the speed of an electron if its location is known to within m (the diameter of a hydrogen atom)?

20. Example
What is the uncertainty in the speed of an electron if its location is known to within m (the diameter of a hydrogen atom)?

21. Example
What is the uncertainty in the speed of an electron if its location is known to within m (the diameter of a hydrogen atom)?

22. Example
What is the uncertainty in the speed of an electron if its location is known to within m (the diameter of a hydrogen atom)?
Obviously there are some problems with our Bohr model of well-defined orbits

23. Question
If light waves are particles (with momentum), does this mean that other particles are waves too?

24. Question
If light waves are particles (with momentum), does this mean that other particles are waves too? A graduate student named de Broglie hypothesized that they were. (And his Ph.D. was held up for a year because it was such a radical idea.)

25. Electron Diffraction
That particles are also waves can be shown experimentally: electrons diffract too.

26. de Broglie Wavelength
Since for photons,

27. de Broglie Wavelength
Since for photons, For any particle,

28. de Broglie Wavelength Since for photons, For any particle,
Note that the more massive the particle, the smaller its wavelength.

29. Example
What is the de Broglie wavelength of an electron with a speed of 3.0 x 106 m/s?

30. Example
What is the de Broglie wavelength of an electron with a speed of 3.0 x 106 m/s?

31. Example
What is the de Broglie wavelength of an electron with a speed of 3.0 x 106 m/s?

32. Example
What is the de Broglie wavelength of an electron with a speed of 3.0 x 106 m/s?
Note that this wavelength, while small, is larger than the radius of a hydrogen atom (1.0 x m).

33. Example
What is the de Broglie wavelength of an electron with a speed of 3.0 x 106 m/s?
Note, however, that the wavelength is less than that of visible light.

34. Electron Microscopes
Since electrons have a small wavelength, they can be used to resolve images of small objects. You can read more about electron microscopes on pages 616 – 618.

35. Sample Image
Mosquito eyes

36. More Practice
Textbook questions
p. 614 #1, 4, 5
p. 653 #3

37. Some Videos http://www.youtube.com/watch?v=IOYyCHGWJq4