Physics 43
Watch these videos. TAKE NOTES on MIT lecture. This substitutes my lecture I cancelled.
1. Mechanical Universe: Intro to Quantum (you have to rewind it)
https://www.youtube.com/watch?v=STJbtg-p4EA&list=PL8_xPU5epJddRABXqJ5h5G0dk-XGtA5cZ&index=50
2. MIT Lecture on Uncertainty Principle
https://www.youtube.com/watch?v=MeK0DV329mU
You will want to review interference and diffraction of light for this assignment and for the topic of Quantum
in general. Note that our book is using
for the uncertainty principle, which is an approximation.
We will use the real equation:
, which is what is used in MIT video I assigned. A full derivation
can be found here https://www.tjhsst.edu/~2011akessler/notes/hup.pdf if you are interested. We will discuss
several interpretations but not do a rigorous derivation because it requires advanced math.
The take home quiz is below. It is based on videos and the section in chapter 39 on uncertainty. Print it out as
usual. Due weds, March 8. Do not wait until the day before to do this as it is a bit deeper than usual which of
course makes it more fun.
We will start with wave functions from chapter 39 next week so read or review that before Wednesday. Read
the first four sections of chapter 40 on 1-D Quantum. We will just barely start it but it will help you see where
the wave functions are coming from that are started in chapter 39. Oh boy here we go!
Quantum time!
Physics 43 Spring 2017 Quiz 6
50 points
Name: __________________________________________
1. In the MIT lecture by Walter Lewin, he demonstrates the uncertainty principle with a laser and a single slit.
Summarize his results. He says he made two calculations showing that if the width of the slit was a 5 microns
or 1 micron, then he could find the width of the central bright fringe. Reproduce those calculations. Explain
how single slit diffraction demonstrates the uncertainty principle, that is, how does the width of the slit and
the spreading of the light demonstrate the Uncertainty Principle. Use a diagram of single slit diffraction
apparatus with the fringe pattern and intensity amplitude to help your explanation. Please print neatly and
clearly. Box answers. Use all this space to do it nicely. It is a very cool and important result. Respect!
2. In the double-slit experiment, electrons are fired at an opaque barrier having two small slits, and a screen
beyond the barrier records where the electrons hit. After many electrons are fired, the standard interference
pattern is shown on the screen. If the electrons are fired with a higher velocity, the spacing between the dark
fringes on the screen will A) decrease. B) increase. C) remain the same. EXPLAIN YOUR ANSWER.
3. You want to confine an electron in a box in such a way that you know for certain that the electron's speed is
no more than 67 m/s. What is the smallest box in which you can confine the electron?
4. An electron is trapped in a quantum well which is 48.6 nm wide. Calculate the minimum uncertainty in its
velocity.
5. A 4.2 × 10-13 gram grain of dust has fallen into the hole shown in the figure and appears to be at rest but by
the Uncertainty Principle we know it cannot be. Does this particle have enough energy to get out of the hole?
If not, what is the depth of the deepest hole of this width from which the particle would have enough energy
to escape? Show your work and justify your answers.
6. In the Mechanical Universe Video Caltech professor Dr. Goodstein does a demonstration about polarized
light. How the heck does that explain the ‘new physics’ or quantum weirdness? Briefly and neatly describe
what he was demonstrating and what it might mean.