Great physics simulations ...

Great applets from Univ. Colorado, including some very nice ones related to the quantum mechanics we're doing now. Check out the Quantum Bound States and Quantum Tunneling applets in particular.

I'll demo a couple of these tomorrow to save you from my crude sketches on the board ...

PH253: Thursday's quiz

As I mentioned yesterday, Thursday (tomorrow), there is a quiz.

• Same material as exam 1.
• You can bring a formula sheet; same rules as the exam.
• One problem.
• The quiz grade will replace the lowest-scored problem on the exam. If you have a very high exam grade, I'll count it toward the homework. It will count toward your lowest non-dropped homework.
• It will take about 15 minutes.
• You should study the exam problems. 
• You can still do 4b from the exam for yet more points.
• If you are satisfied with your grade so far, you do not have to bother.
• It will happen at the end of the class period.
• If you can't make it to class, you should document your reason in some fashion.

Hopefully that's everything ... let me know if you have questions.

PH253: Supplemental texts

If you're looking for some additional reading, I can recommend two more supplemental texts (in addition to the Feynman Lectures on Physics I already recommended):

One is the Serway book used in PH105 and PH106. If you know someone with the full double volume (it is in the Rogers library too), the last chapters are very much the same as what we're covering now. (Physics for scientists and engineers with modern physics / Raymond A. Serway, John W. Jewett, Jr.). I would guess that it is pretty easy to find someone that has this book left over from PH106, and there should be multiple copies in the Rogers library since it is a book we've used for a long time.

Another very good book, one I came close to using this semester, is the one by A.P. French (An introduction to quantum physics / A. P. French, Edwin F. Taylor.), which is also in the Rogers library. The mathematical level is at times a bit higher, but the explanations and examples are I think very clear. Some of the problems from your homework come from this book in fact, and I would probably recommend it over the Serway book for understanding the qualitative aspects.

In similar news, I am going to try to tie the homework problems to each Tuesday's lecture a little more closely so I can spend a larger portion of the in-class time on homework problems. This time around, most of the problems relate directly to stuff that I'll go over in Tuesday's (er, today's) class, and I'll try to make that the case most of the time.

(Also, as a reminder: if you click on an event in the course calendar (look to the right side of the page), and ask to "show event details," the relevant sections of the textbook for each lecture are listed.)

PH255: heavy updates to the lab manual

Primarily, the procedures for the resistivity/noise (called "rho-mu" in the schedule) and fine structure in atomic spectra now exist. A few other clean-ups as well.

Additionally, for the resistivity/noise lab you will find useful papers and sample code in the templates directory.

PH253: HW 5 is out

Homework 5 is now out. Since I'm a little late in getting it out, you can turn it in Friday instead of Thursday.

Recall that you can turn in problem 4b from Exam 1 for an additional 1.5 points (5%) on Exam 1. You can turn this in with HW5 (at the latest). 

PH253: extra credit

Tuesday, I'll announce an extra-credit mechanism for you to make up points on the exam. Once I figure out what it is ;-)

So, rest easy,  and have a good weekend.

PH253: Exam 1 results

The exam scores are in. You'll get them back in class on Thursday; see the previous post for how to check the scores online.

There is of course good news and bad news. The good news is that I think most of you are getting the concepts, but there are a few specific points we need to go over. The bad news is somewhat more multi-faceted.

Checking grades online

I now finally have the system set up so you can log in and see your grades. Instructions below the jump ...

PH253: Thursday's class

That's all for tonight. I should have the exams graded and returned to you on Thursday (along with HW3), given that I finished half the grading after dinner.

For Thursday's class, we'll go over the exam, and then talk about more solutions to the Schrodinger equation (square well, tunneling). For that, you should finish reading section 2. Next week we'll get to the Bohr model, the start of section 3.

(About the poll on the right: just for my curiosity. Answer honestly, it is anonymous.)

PH253: Exam note #3

Through the first three problems, I am guessing I will have to scale the exam a bit. Number 2 was the best of the three, probably owing to the very similar practice problems.

One thing to note: the practice problem most relevant (#10) had one mass-less decay product, on the exam question that was not true ... similar problems, but not quite identical. The main difference is that E=pc only works for massless particles.

On the exam problem, since the decay products were identical in mass, and the parent started at rest, the two decay products must have equal and opposite momentum. Thus, their velocities must be equal and opposite, and their gamma factors the same. If that is true, the two decay products must have the same energy. Energy conservation then equates the rest energy of the parent (Mc^2) with the total energy of the two decay products. Since the two products have the same mass and gamma factor:

Mc^2 = \gamma_1 m_1c^2 + \gamma_2 m_2 c^2\\M = m \left(\gamma_1+\gamma_2\right) \qquad (\text{since } m_1=m_2\equiv m)\\
M = 2m\gamma \qquad (\text{since } \gamma_1=\gamma_2\equiv\gamma)\\
\frac{v}{c} = \sqrt{1-4m^2/M^2}

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.

PH253: Exam, last-minute things

Don't forget your calculator ... there are not many numbers on the test, but just enough.

Today

I'll be in Gallalee all day. From 2-5pm, I"ll be in room 322 running a lab, but feel free to come by for quick questions.

PH253: more practice problems

UPDATE 5: some typos fixed, particularly one in problem 10 just above equations 36-39. The sentence fixed was "The muon has both kinetic energy and rest energy, and we can write its total energy in terms of ..." The prior version said "... write its total kinetic energy ..." which is incorrect.

UPDATE 4:  all problems should have solutions now. I also realized that partial derivatives are beyond the stated math prereq, so you can ignore problem 11 ... something like that will not be on the exam.
UPDATE 3:  answers for all but 11 are included and some typos in the problems fixed.
UPDATE 2:  answers for all but questions 6, 8, 11 are there.
UPDATE: answers for about half the problems are up now. Should have the rest done in an hour or so.

Here you go. These are much closer to real exam problems. Read the general comments as well: one or two of these problems might just show up on the exam with little or no modification.

Answers & some solutions will follow later today.

UPDATE: I scratched the first problem (density and so forth) on further reflection.

PH253: Exam practice problems

Just to get you started, here are some questions from the text that are worth looking at:

Section 1:

• Example 1.7
• Exercises 3,4,5,6,12
• Problem 6

Section 2:

• Exercises 3, 11, 12
• Problem 3

These are relatively simple problems, but concerning topics that are very likely to show up on the exam. I'll be posting some more in-depth problems shortly for you to practice on. These will very closely resemble what the exam will look like.

Thanks ...

... to many of you for sending in sensibly-named files :-)

Example test problems coming tomorrow. For now, check out this, and this.

If you're not feeling mathy, try some animations. This page has some nice ones that let you see the difference between phase and group velocity nicely, as well as how the wave packet spreads (so you can see how the uncertainty in localizing the associated particle changes).

Research Opportunity

A colleague just asked me if I knew any undergrads interested in spending the summer doing an internship at Argonne national lab. The project would involve developing an electrostatic switch using ultrananocrystalline diamond films. If you don't know what that means, it would be working with a lot of really cool vacuum and electronic equipment. :-) Travel money and stipend are likely to be covered.

If you were thinking about a research internship for the summer, and have an interest in the solid state physics or ECE areas, it might be something worth looking in to. Let me know if you'd like to know more, I'll put you in contact with my colleague.

HW4.8a

Your energy should be more on the order of 0.1GeV, not 1.0GeV as I stated earlier ...

HW4

Tomorrow in class, I'll spend extra time going over problems 2, 4, and 8 (and will try to post further hints tonight). I think those are the trickier problems with the most subtlety involved. Several of the others just have one silly trick you might not have caught yet, and will probably not seem so bad once you know the trick.

Also: my view on homework is that if you don't learn something by doing it, everyone's time is wasted. Given that, don't feel bad if there are problems you're not getting right away. If you understood it all right off the bat, there would be nothing to learn.

Formula sheet (quick draft)

Here's a rough draft of the formula sheet for the exam, to give you an idea. I have not yet proofread it carefully, nor checked to be sure that I don't want to add or subtract a few things. It is unlikely to change noticeably, but just a heads-up. Any odd integrals/derivatives you need for specific problems will be provided within the problem itself, you will not be expected to memorize arcane calculus formulas (just basic ones).

At least a day or two before the exam, I will post an updated version if there is one. What you see so far is a good indication of what you do and don't need to put on your own formula sheet, however.

If you notice any typos/errors/odd omissions, please let me know.

PH253: scanned notes

I've scanned my own lecture notes (most of them anyway) and put them here as PDF files. They cover most of the material since relativity (and a bit of that). For the beginning bits of relativity, see here.

Hopefully, you can read everything and decipher my crude drawings ... let me know if you have questions. If you're using them to fill in the gaps in your own notes or augmenting the text, it will probably be OK. If you're relying on them as a sole source ... not so much.

HW 3 solutions

Here you are. Let me know if you find any mistakes, or would like further clarification ...

Plan for Thursday

Thursday, we'll do 3 things:

1) Restate the motivation for the form of the Schrodinger equation, since it went fast today.
2) Look at a couple of simple solutions to the Schrodinger equation.
3) Spend about half the time setting up problems from HW4 (or previous HW if you like)

The reading would be 2.4.3-2.4.8. Also: you click on an event in the course calender and ask to show more details, the reading for each lecture is listed already.

Homework 4 hints

Most of the homework should make sense after Tuesday's lecture, if not already. Here are some hints to get you started.

1) Write w as a function of k and differentiate. Re-write the derivative in terms of p (substituting for k), and use the relativistic form of momentum to get everything in terms of c and v. Should work itself out.

2) The dropped ball will have some random horizontal velocity due to uncertainty, which gives a spread in x. Get the momentum uncertainty from this initial uncertainty in x, which gives you the velocity uncertainty. The final uncertainty in horizontal position is then governed by normal mechanics - final position is initial position plus velocity times the time required to fall a distance H. Once you have an expression for the final spread in x, differentiate with respect to initial uncertainty to minimize. We'll go over this in class, it is sneaky.

3) Plug and chug. Momentum is (gamma)mv, plug that in de Broglie. Simplify, and define the Compton wavelength to be h/mc.

4) The uncertainty relationship gets you momentum uncertainty from a given position uncertainty. Best-case scenario: the position has its minimum uncertainty value (Delta)x. Get E in terms of x, differentiate, and plug the extremal x value back into your energy equation.

5) There is an extremely good chance that these lines correspond to the emission spectrum of a simple element. If you figure out which one, subsequently figuring out all the combination is far easier.

6) The de Broglie wavelength is h/mv. The average velocity from kinetic theory is:

\langle v \rangle = \sqrt{\frac{3k_BT}{m}}

There go you. Note that the mass of a helium atom is about 4 atomic mass units. Also note that this is a problem from your text, i.e., the numerical answer is in the back of the text.
7) Huh. Nearly what we did in lecture :-) You may also find the MIT course 8.04 Open Course Ware (OCW) interesting. What's different about the helium ion?

8) We'll go over this one in class. Again related to the MIT 8.04 OCW.

Emailing documents / Minor Rant

I'm not quite sure how to point this out without exuding self-entitlement and so on ... so I'll just put it out there.

As of tonight, I have about 25 new documents from this evening entitled 'homework' or 'homework_3' or 'hw' or some variant. I have little folders with your names that contain these documents in order to keep them straight, and a hierarchy of folders to distinguish different homework sets. There is a complicated system in place. Worst case, I can always go back to the original email if I am not 100% sure. So far, and for the last few semesters, it works. I also try to acknowledge receipt as quickly as possible.

However, it would save a lot of time for me if the files you sent me contained your last name in some way. When I get a file named "homework.pdf" I can't just hit "save attachment" and select the homework directory, or chaos ensues. If isn't a huge inconvenience, naming the files cleverly before you send them to me helps a lot. Again, I'm not suggesting my time is more valuable than yours, but there are roughly 25 of you submitting homework electronically and one of me. Another good thing is to make sure your name is written on the first sheet before you scan, that is another helpful failsafe.

I don't mean to inconvenience you - I will still accept files labeled "homework.pdf", "physics.pdf", and "SCN9211523.pdf" if you can't do otherwise, and will meticulously keep track of who sent which files when, but you can help make this process more efficient.

Don't get me wrong, I do really love the electronic homework. Giving you the ability to attach Excel or Matlab files to solve numeric problems is much more efficient for both of us, if that is your preferred mode of solution. It also eases the communication barrier and time pressure, I think. There is something really cool about getting homework submitted via iPhone, for instance, or receiving a nicely-formatted spreadsheet, I have to admit. My main point is that more options can breed more obfuscation if you're not careful. While I can deal with a myriad of file formats and odd file names, the next person might not bother ... e.g., applications for jobs or internships.

Finally, there is nothing wrong with hard copies shoved under my door. Don't feel pressured to submit electronically or make complex spreadsheets if you prefer pencil and paper. I'm just leaving that as an option for you, if that's how you roll.

Additional reading that might help

The last couple of lectures I've done have made use of the Feynman Lectures on Physics, volume III, chapters 1&2. Highly recommended if you want some additional background.

Foo

We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover all the tracks, to not worry about the blind alleys or to describe how you had the wrong idea first, and so on. So there isn't any place to publish, in a dignified manner, what you actually did in order to get to do the work, although, there has been in these days, some interest in this kind of thing.

- Richard Feynman, Nobel Prize Acceptance Lecture, 1965

PH253: HW4 is out

Exiting, I know, but here it is. Due one week from today. Owing to the exam the following week, there will not be a new homework set next week, HW5 will not come out until after the exam.

UPDATE - the title of the homework was incorrect earlier (listed as HW3 solutions), that should be fixed now. Blogger was having problems earlier (still?) with links being broken as well.

PH253: Thursday's class

Later this morning, we'll rehash the double slit experiment and move on to the 'wave-like' properties of matter and their consequences. We won't get as far as probability amplitudes yet (maybe through 2.4.3), but you should read the rest of Chapter 2 section 4 (2.4) by Tuesday.

P255: photoelectric experiment

Some details on the detector used, such as what the work function should be.

File this away for report-writing time ...

PH253: Homework 3 hints

Here are a few hints to get you going, I'll post some more later tonight.

#1 - really just unit conversion ...
#2 - if you use energy & momentum conservation, you should come to a ridiculous conclusion. For instance, if you write the energy and momentum of the electron in terms of gamma, try solving for the electron's velocity ...
#3 - conserve momentum. The velocity will be very small (but measurable with the Mossbauer effect, which we'll get into later).
#4 - there is only one thing different compared to normal Compton scattering. It is that easy.
#5 - Rewrite the Compton equation substituting energy in place of wavelength appropriately. The energy difference E_i - E_f will be a function of E_i and E_f, and that is OK. Proportional to both, in fact.
#6 - just do what I suggested in class ;-)
#7 - from frequency and speed, you can get wavelength. The total energy per unit time is just power, which is the energy per photon times the number of photons per second. It is a stupidly large number of photons.
#8 - plot + regression ("trend line" in business-speak). Note that the slope of the stopping potential (y) versus frequency (x) gives you h/e, not just h! Multiply the slope by e=1.6e-19 to get h in familiar units.
#9 - you can use your result from #5. If the electron is initially at rest, its energy is just its rest energy. You want to find the change in energy divided by the incident photon energy. As we discussed in lecture, the energy shift should be much larger percentage-wise for higher energy incident photons.

Today

Today I should be in Bevill from about 10:15-12, and in Gallalee the rest of the day and free from 1-3 and 5-6.

Nice particle physics handout

Courtesy MIT course 8.033. Some relevance to what we've been covering lately ...

PH253: Exam 1

Exam 1 is coming up in 2 weeks, 16 Feb 2010. Here's what it will cover:

Sects. 1.1-3, 5 (Relativity, excluding 1.4)
Sects. 2.1-3 (quantum hypothesis, photoelectric, photons)
Sections we did not cover in class which you are responsible for: 2.1.7, 2.2.4, 2.3.1

The material we cover for the next 3 classes will mostly not be on the test. Specifically, it will not cover 2.4. The format of the exam will be 5 problems (i.e., solve, no multiple choice), you pick any 4 to solve. Put another way, I'll give you 5 problems, you can skip any one of them you like.

I will provide a formula sheet with all relevant constants and basic formulas which should be enough to solve all problems. Additionally, you are allowed to bring in a single 8.5x11 inch sheet of paper with your own notes, formulas, etc. -- anything you want, really. Front and back sides are allowed, I will allow two sheets with only a single side if you prefer that. You are additionally allowed writing implements and a calculator (i.e., not a cell phone or any network-enabled device). You can feel free to program your calculator in arbitrary ways, however, just no internet or peer-to-peer communication.

More details and sample problems will follow in the next week. For now, I suggest reading the chapters and homework solutions.

PH255: Stats/uncertainty resources

Here's a good page from MIT's advanced lab. There is a primer on uncertainties, and a shorter guide on curve fitting (regression).

Worth checking out the rest of their site as well. Many aspects of the revised PH255 course were based on what MIT does in their 8.13/8.14 courses.