Tuesday's lecture, evaluations

Today, in about 10 hours, we will figure out how lasers work. That's our last regular lecture, Thursday's lecture is still up to you, to an extent.

If you don't like lasers, here's another reason to attend: we'll do the department's discursive 'free-form' course evaluations at the end of the lecture. A good chance to give some (totally anonymous) feedback on what you'd like to see done differently, or not. I really do read all the evaluations and adapt based on the feedback.

The discursive evaluation is in addition to the online evaluation form for course evaluation you should have received email about already (probably a couple of times). Currently, only 26% of you have done the online evaluations, so please, please check your email (search for SOI if you have a lot of email) and fill out the college-wide evaluation. It takes 10 min at most, it is completely anonymous, and like the discursive evaluation, I take them very seriously when planning my courses.

PH253: what is the point of HW9?

This week's homework is difficult, I grant you that, but not without reason.

*The first two problems are really our first stab at calculating the properties of real, everyday, useful materials (not that H is not useful or interesting, I guess). The vibrational frequency you'll calculate for KCl matches experiments amazingly well, in spite of the simple model potential used.

* The variational principle is something you will come across again, probably in mechanics (PH301/2) if not quantum. It is more or less a powerful way to come up with a best guess solution to a problem without actually solving it, and therefore powerful. There exist even more powerful methods commonly used in Chemistry and Physics for calculating the electronic properties of materials (e.g., Hartree-Fock, Density Functional Theory), but they are far more difficult. Should you encounter them, you're likely to be thrown in the deep end; the point of problems 3&4 is to give you a taste of how to handle systems which cannot be treated exactly without all the mathematical baggage that can obscure the essential simplicity of the method.

* Coupled oscillators can be used to explain a really ridiculous number of phenomena. In Thursday's lecture, we'll used a coupled oscillator model to (more simply) re-derive all of what we've learned of bonding, and cast it in a form that looks suspiciously like masses & springs or coupled LC oscillators. With this new approach, we'll be able to extend our analysis to the case of periodic solids (like semiconductor crystals, leading us to transistors and such). We'll be able to explain why some stuff is electrically conducting and other stuff is not, and why real materials behave the way you do. Problem 5 is meant to get you thinking about how coupled oscillators work as a preface to that lecture. It also gives you some hints on how one can spectroscopically identify different molecules (look for radiation emission/absorption matching the vibrational frequencies) or when molecules are adsorbed on a surface, e.g., in catalysis (new vibrational modes show up compared to the original molecule).

So, in short (if it isn't too late for that), think of this problem set as a preview of what's to come - both how we'll figure out how to calculate the properties of real materials, and what you're going to be up against in later courses. Most of what we've done the last month or two has been leading up to this.

Physics tutoring

Two options:

1) I am going to negotiate with the grad students running the physics help desk to let you go to their hours for help. They are only expected to help out with 100-level physics at the moment, but I think they'd be happy to help. Presume you can go to their office hours listed in the link above unless I tell you otherwise ...

2) The physics student society runs study sessions every Sunday evening at 6pm in 109 Gallalee. It is not organized per se, but a group of physics students that get together to work on homework collectively. A lot of them are upper-level students who have already been through PH253, so they can help. I've talked to them, and they are happy to work with anyone who shows up. The main entrance is locked on Sunday, but usually they will have someone manning the quad-side door periodically to let people in. This might be the even better option, sometimes getting some help from someone who was in your position not so long ago is the best.

Special colloquium next week!

Next week, on Thursday, 30 September at 7:30pm, we are having a very interesting public talk in 227 Gallalee:

"What Every Dog Should Know About Quantum Physics" by Dr. Chad Orzel of Union College

Chad Orzel is the author of a popular physics blog called Uncertain Principles: http://scienceblogs.com/principles/

and the author of a book titled "How to Teach Physics to Your Dog"
http://dogphysics.com/book_info.html

Chad Orzel's bio can be found here:
http://dogphysics.com/about_chad.html

Here is an abstract for Chad's public talk:

Quantum physics, the science of extremely small things like atoms and subatomic particles, is one of the best tested theories in the history of science, and also one of the most bizarre. Many of its predictions -- particles that behave like waves, cats that are alive and dead at the same time, objects that pass through barriers as if they weren't even there -- seem more like science fiction than science fact. This talk will explain the reality behind some of the stranger aspects of quantum physics, and why it is so important that even dogs should know about it.

PH255: Writing a scientific paper

Lab reports are a real pain, and I know many of you in PH255 have been struggling with how to go about writing a lab report. Here's how I usually go about writing a paper:

PH253: Exam note #2

On Thursday, it is crucial that we discuss series expansions briefly. Very handy little things that will come up more and more often, and judging from the number of people skipping problem 3, something you haven't been exposed to much.

Try to remind me of this when we go over the test on Thursday :-)

Also, I am apparently live-blogging my exam grading. This is deeply strange.

PH253: Exam note #1

A quantity like "35000 revolutions per minute" is an angular velocity. Say you have disc spinning at an angular velocity (omega), and you are interested in the linear velocity at a point a radial distance r=0.1m from the center of the disk. The velocity calculation goes like this:

v = r\omega = \left(0.1\,\text{m}\right)\left(35000\,\frac{\text{rev}}{\text{min}}\right)\left(\frac{1\,\text{min}}{60\,\text{sec}}\right)\left(2\pi\,\frac{\text{rad}}{\text{rev}}\right)\approx 370\,\frac{\text{m}}{\text{s}}

First, you need to convert the angular velocity to radians per second (or just 'per second' since radians are really just a ratio, and thus unit-less). Then you can multiply by the radial distance from the point of rotation to get the regular velocity or speed at that point on the disk.

That's my main comment on problem 1 of the exam. The second one being that the time dilation factor is just the ratio between the time elapsed at the rim of the disc to that at the center (which is at rest). The ratio is just (gamma) - we don't need to use the full Lorentz transformation, because there is no significant spatial separation, and we are talking about different parts of the same object.