1. Photons and QM III Introduction Quiz
Niels Bohr and Albert Einstein “chilling out” and discussing QM (Quantum Mechanics)
Introduction
Quiz
Heisenberg Uncertainty Principle (applied to photons).

2. Review of Big Picture Concepts
Q: What physical phenomena demonstrate that EM radiation (e.g. light) behaves like a wave ?
Ans: Interference and Diffraction.
Q: What physical phenomena demonstrate that EM radiation (e.g. light) is made up of particles ?
Ans: Photoelectric Effect and Compton Scattering are two examples. Cutoff in bremsstrahlung energy spectrum is another.

3. Bohr’s principle of complementarity
1928: The wave descriptions and the particle descriptions of nature are “complementary”. We need both to describe nature, but we will never need to use both at the same time to describe a single part of an occurrence. 3

4. Scene from the foundations of quantum mechanics.
: In this period, Niels Bohr and Albert Einstein had many discussions about quantum mechanics.
Einstein: “God does not play dice with the universe”
Bohr:
Einstein stop it !
Stop telling God what to do ! 4

5. Today: Heisenberg’s Uncertainty Principle
Some “left-overs” on Compton scattering/pair production.
We will then read the original 1927 paper in German by Heisenberg.
Not joking: Will have some extra (4) clicker questions towards the end of class to check your understanding of the Heisenberg uncertainty principle. 5

6. A minimum frequency of light is generated
In photoemission, a fast moving electron hits a metal and generates light. The experiment results show that there is
A minimum frequency of light is generated
A maximum frequency of light is generated
All frequencies of light are generated
All wavelengths are generated.
B) For bremmstrahlung

7. A minimum frequency of light is generated
In photoemission, a fast moving electron hits a metal and generates light. The experiment results show that there is
A minimum frequency of light is generated
A maximum frequency of light is generated
All frequencies of light are generated
All wavelengths are generated.
B) For bremmstrahlung

8. Electron-positron (e+ e-) pair production can occur for
Q17.2
Electron-positron (e+ e-) pair production can occur for
Any photon energy
Photon energy above 2 mec2
Photon energy above 2.5 mec2
Photon energy below 1.9 mec2
B (the photon must carry energy to compensate for the electron-positron rest mass).

9. Electron-positron (e+ e-) pair production can occur for
Q17.2
Electron-positron (e+ e-) pair production can occur for
Any photon energy
Photon energy above 2 mec2
Photon energy above 2.5 mec2
Photon energy below 1.9 mec2
B (the photon must carry energy to compensate for the electron-positron rest mass).

10. Same frequency as the incident light
In Compton scattering, light hits an electron and bounces off at an angle from the incident direction. The electron was initially at rest, but gains momentum from the scattering. The scattered light has the
Same frequency as the incident light
Higher frequency than the incident light
Lower frequency than the incident light
Half the frequency of the incident light
C lower frequency (higher wavelength) and lower energy, remember E=hf 10

11. Same frequency as the incident light
In Compton scattering, light hits an electron and bounces off at an angle from the incident direction. The electron was initially at rest, but gains momentum from the scattering. The scattered light has the
Same frequency as the incident light
Higher frequency than the incident light
Lower frequency than the incident light
Half the frequency of the incident light
C lower frequency (higher wavelength) and lower energy, remember E=hf
Lower frequency (larger wavelength) and lower energy, remember E=hf 11

12. Q17.4
At what angle ϕ is the outgoing photon wavelength half of that of the incoming photon?
0 degrees
30 degrees
45 degrees
60 degrees
C lower frequency (higher wavelength) and lower energy, remember E=hf 12

13. Q17.4
At what angle ϕ is the outgoing photon wavelength half of that of the incoming photon?
0 degrees
30 degrees
45 degrees
60 degrees
ϕ= 60 degrees
C lower frequency (higher wavelength) and lower energy, remember E=hf
½ = C(1-cos ϕ)
½ = cos ϕ 13

14. Q17.5
In Compton scattering, a photon has both energy and momentum. What are expressions for the photon energy (E) and the magnitude of the photon momentum? D 14

15. Q17.5
In Compton scattering, a photon has both energy and momentum. What are expressions for the phonon energy (E) and the magnitude of the photon momentum? D 15

16. Entering an Uncertain Universe…
“Breaking Bad” TV series: Heisenberg, evil alter ego of Walter White, meth dealer. 16

17. Left overs: Compton scattering in “real life”
“Tight”
“Loose” 17

18. Compton scattering example
An photon with a wavelength of 0.100nm collides with an electron initially at rest. The x-ray’s final wavelength is nm. What is the final kinetic energy of the electron ?
Energy is conserved 18

19. Compton scattering example (result in Joules and keV)
A photon with a wavelength of 0.100nm collides with an electron initially at rest. The x-ray’s final wavelength is nm. What is the final kinetic energy of the electron ?
Question:: How do you convert to eV ?
Ans: Remember 1 e =1.6 x C 19

20. Compton scattering conceptual question
Question: Do you expect to notice a wavelength shift in Compton scattering from visible light ?
Yes/No ? Why ?
Ans: No, the quantity h/(mec)= 2.42 x 10-12m = nm. Compare to visible light wavelengths nm.
The effect is much more dramatic with X-rays. 20

21. Pair production by a single photon
Question : Why are the two tracks curving in opposite directions ?
Ans: Particle and antiparticle have opposite charges ? 21

22. Let’s think about formation of Optical Images
The point: Processes that seem to be continuous may, in fact, consist of many microscopic “bits”. (Just like water flow.)
For large light intensities, image formation by an optical system can be described by classical optics.
For very low light intensities, one can see the statistical and random nature of image formation. Use a sensitive camera that can detect single photons.
A. Rose, J. Opt. Sci. Am. 43, 715 (1953)
A. Rose, J. Opt. Sci. Am. 43, 715 (1953)
DEMO:
428 Geiger counter 22
Exposure time

23. Diffraction and the particle nature of light
A diffraction pattern is the result of many photons hitting the screen. The pattern appears even if only one photon is present at a time in the experiment. 23

24. Diffraction and uncertainty
A diffraction pattern is the result of many photons hitting the screen. The pattern appears even if only one photon is present at a time in the experiment.
Question: Diffraction is the result of the wave nature of light ? How is this possible ?
Ans: Light is both a wave and a particle. Different measurements reveal different aspects. “Complementarity”. 24

25. Diffraction and the road to the uncertainty principle
When a photon passes through a narrow slit, its momentum becomes uncertain and the photon can deflect to either side A diffraction pattern is the result of many photons hitting the screen. The pattern appears even if only one photon is present at a time in the experiment. 25

26. Diffraction and uncertainty
Question: What is the location of the first minimum in single slit diffraction ?
In the small angle approximation
Although photons are point particles, we cannot predict their paths exactly.
All we can do is predict probabilitiesThere are uncertainties in their positions and momenta 26

27. Uncertainty in momentum and position (rough argument)
What is the uncertainty in the momentum of each photon ?
~85% of the photons lie in the angular range between [+θ1 , -θ1]
Using the small angle approximation
The average value of py is zero.
However, the value of py is uncertain 27

28. Uncertainty in momentum and position (rough argument)
How are uncertainties in the momentum and position of each photon related ?
Here a is related to the uncertainty in the y-position of the photon while Δpy is the y-momentum uncertainty.
Question: What happens to the width of the central maximum in diffraction when the slit width a decreases ?
Ans: The peak becomes broader. What does this mean for uncertainties ? 28

29. Heisenberg Uncertainty Principle (exact result)
How are uncertainties in the momentum and position of each photon related ?
Here Δx and Δpx are the standard deviation or (rms) uncertainties in x and px
The quantity on the right is “h-bar” over 2.
Warning: “h-bar” is not the same as h 29

30. Heisenberg Uncertainty Principle (another version)
How are uncertainties in the energy and time localization related ?
Here ΔE and Δt are the standard deviation or (rms) uncertainties in E and t.
The quantity on the right is “h-bar” over 2.
In Chapter 39, we will see that the Heisenberg uncertainty principle also applies to matter particles 30

31. For next time Quantum Mechanics  on to particles
Read material in advance
Concepts require wrestling with material