Built on Facts

Archives for May, 2009

Sunday Function

Nobody ever asks the interesting questions at presidential press conferences. But if somehow I could choose a question, it would be this: “Mr. President, has the NSA solved the integer factorization problem?” Of course it’s unlikely he’d know off the top of his head, and even if he did he certainly wouldn’t give me an…

Jon & Kate Plus 10,000,008.

There’s a lot of important things going on in the world. Kim Jong Il is exploding nukes and launching missiles over Japan. A Supreme Court justice has been nominated. The treasury bond market experienced its steepest yield curve ever. Whatever. Today we talk about Jon & Kate Plus 8. Jon and Kate, should you have…

A few days ago we had an interesting discussion about the actual nature of light waves with respect to the informal qualitative presentation of light waves found in intro textbooks. Because I have the best set of physics blog readers in the world, a fascinating discussion ensued with CC and Neil among others. One of…

Continuing from yesterday’s post on approximation methods in quantum mechanics, here’s another common method worth a close look. It’s one of my favorites, because it’s a rare technique in which you can just make something completely up from thin air and it will very probably work well nonetheless. Let’s say you have a particle floating…

We haven’t done an actual straight-up physics problem in a while, much less one above the level of undergraduate freshman physics. There’s a reason: it’s roughly as niche as it’s possible for an internet post to be. But on the other hand, surely someone ought to do it every once in a while. So here…

Traffic & Phase Transitions

It’s 10pm on a Sunday night, and I’m driving west on Interstate 10 right through the middle of downtown Houston. Focused on getting to my destination safely, I obey the traffic laws and proceed through the comparatively deserted interstate at the maximum speed allowed by law. To experimentally do otherwise is a bit hazardous, so…

Memorial Day

It is foolish and wrong to mourn the men who died. Rather we should thank God that such men lived. – George S. Patton, June 7, 1945. On this Memorial Day, we remember those members of the armed forces of the United States who have given their lives in the service of this, our Republic.…

Sunday Function

Pick a two-digit number. Anything from 0 to 99 inclusive will work, because the single digit numbers can be considered to have a leading zero. Add the digits together. Subtract that from the original number. So if you started with 12, you add the digits to get 3, and subtract that from 12 to get…

Yesterday we talked about how fermions and bosons had different values of spin and thus their wavefunctions had different symmetry properties. In particular, fermions are antisymmetric under exchange of particles. We’d like to write the overall two-particle wavefunction in terms of the individual wavefunctions for each of the two particles. The result will look like…

Why the exclusion principle?

Last time on Sunday Function we talked about two types of symmetries that a real function might have: odd and even symmetry under reflection about the y-axis. Much more than I expected even as an undergraduate student, these types of symmetries turn out to be of amazingly fundamental importance in fundamental physics. One of these…