Weekend discussions 3

I have a backlog of a few weekends which I hope to catch up with very soon. Anyway, this post is concerned with our discussions yesterday and the day before. So here it is:

September 25, 2010

Session 1: Shruthi

We continued our foray to understand the necessity of a quantum theory, and Shruthi pointed out a few interesting things like whether we could determine the terminal velocity of a steel ball dropped into liquid helium. Th results were more interesting. I think Shruthi will do a better job of discussing that. We then went back to a concept we were all fuzzy about. Matter waves. Superposition. Wave packets. What we all thought was a trivial thing and went right ahead after thinking we understood it, is now coming back to haunt us. I'm struggling to make the problem itself clear. Maybe someone should open it up for discussion here.

Session 2: Raunaq

He said he'd write this himself.

September 26, 2010

Session 1: Karthik

He started off by getting us to discuss what exactly a linear, homogeneous differential equation means. We then worked through the problem of the damped harmonic oscillator, which we went on to study in a matrix representation, finally giving (atleast me) a good idea of exponentiating a matrix. This was followed by a phase space analysis of the problem, at which point Karthik urged us to read up on the Sine-Gordon equation and elliptic functions. He actually wanted to continue next week, but I made him give an introduction to the Poisson bracket as it was previously agreed that I would continue from there. So he did.

Session 2: Harshini

Well, I didn't get to do most of what I'd planned on doing. I started off by basically showing how the Commutator bracket is connected to the Poisson bracket and went on to discuss how these become operators in quantum mechanics. Actually, the problem was I couldn't show how they become operators. Staying true to our policy of not taking anything for granted, we spent a while talking about whether we've missed something in making the leap from something being a physical quantity in classical mechanics, to becoming an 'operator' in quantum mechanics. It doesn't sound quite so serious when put this way, but we struggled over the details for a bit.

Then we followed in the steps of Schrodinger to "derive" the Schrodinger equation, all the time questioning the rationale behind it, and whether it could be done in a better way. Nothing might come out of it, but its very important that these questions are asked. That's what makes what we're doing worth doing.

And before we leave, an ego-check is always done, so that we know that we're not doing anything path-breaking or earth-shattering in these discussions. But what we are doing, is something different.