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).

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.

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

Scene from the foundations of quantum mechanics. 1928-1935: 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

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

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

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

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).

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).

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

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

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

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

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

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

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

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

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 0.110 nm. What is the final kinetic energy of the electron ? Energy is conserved 18

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 0.110 nm. What is the final kinetic energy of the electron ? Question:: How do you convert to eV ? Ans: Remember 1 e =1.6 x 10-19 C 19

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 = 0.00242nm. Compare to visible light wavelengths 380-750 nm. The effect is much more dramatic with X-rays. 20

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

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

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

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

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

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

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

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

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

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

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