Setlist L06 (90 minutes)

Position and Momentum eigenstates Prep: Double slit interference PhET. Particle measurement PhET, Fourier PhET

1. Last class – Interpreting the double slit experiment 2. Start class with Double slit PhET running. Use single particle setting, show wave

function shooting a single photon at a time. We see that it appears as a single dot on the screen. Explain what is happening in detail.

3. Clicker [Q] - Probability photon hits a spot on the screen - D 4. Mathematical model describing the fuzzy blob becoming a dot. We need

something that for every point in space tells us how much fuzziness there is. 5. Clicker [Q] - probability from a wavefunction - C 6. Description of probabilities (usual chemistry would have covered this) 7. Clicker [Q] - Removing middle slit - C 8. Remind them of E = hf and p = h/lambda 9. With determinism thrown out the window, what are the equivalentnt of Newton’s

laws for quantum mechanics? 10. Clicker [Q] - The wavefunction above represents… - D

1. Wave function has complete information about the physical configuration “state” of the system

2. A wavefunction describes one particle with no definite location. 11. Clicker [Q] - If we take a measurement of the state, what does the wave function

look like right after the measurement? - B 1. Use PhET To show measurements!

12. Start simple in describing how this works: Draw a sine wave (wavefunction) with wavelength lambda and momentum p. Ask the class to estimate what the speed v is given that it’s an electron. p = h/lambda, v = p/m. A pure sine wave is a momentum eigenstate! Really confident in the momentum, position is really spread out. (note, not normalizable, the sine wave is an idealized thing, a real particle must go to zero at infinity)

13. Ask class, “What does a position eigenstate look like?” Definite value of position, momentum isn’t well determined.

14. Real travelling particles are somewhere in between position and momentum eigenstates. This is called a WAVEPACKET..

15. Exercise: A travelling electron has momentum p. Draw the least spread out wave packet that could represent this electron.

16. Wavepackets are the sum of a bunch of different eigenstates. Being well defined in one pictures means being undefined in another picture.

17. Heisenberg uncertainty principle. 18. Clicker [Q] - Which spreads out the fastest? - A