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Date: 2007-12-26 01:12
Subject: (More than a) Slight detour - Part #3: Gauge Invariance, Bohm-Aharonov effect and Landau levels.
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Sorry it's been 6th months since the last one of these. I've been a little swamped with school. Good news is, it's full steam ahead, now!

So, eventually, I still intend to make a post about how Hamiltonian mechanics gives us the Schrodinger equation, but in the meantime, let's pick up where we left off. I'm mainly making these posts for my own education, but maybe someone on my friends list will get some use out of them too. I also have a bunch of other posts in mind, but there's already too much on my plate, so we'll see what happens.

I stole this material from here. For a discussion about how all this relates to something called "Berry's phase," check out section 10.2.3 of Griffiths.

The Bohm-Aharonov effect, let me show you it! Landau levels, too!Collapse )

P.S. A late Merry Christmas to everyone on my friends list.
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Date: 2007-06-15 00:19
Subject: Slight Detour -- Part #2: The Lagrangian of a Charged Particle in an EM field.
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Here's the continuation of the last post, where we look at the problem I mentioned and see where it leads. (90% of this material is stolen from Griffiths E&M book. I blame Asma.)

The Lagrangian of a Charged Particle in an EM field.Collapse )
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Date: 2007-06-13 12:36
Subject: Slight Detour -- Part #1
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So, I know I still haven't finished the second half of that earlier physics post, where we'll derive the Schrodinger equation from classical mechanics, but I thought I would take a little detour first. There was a problem that's been bugging me since the middle of last semester. I asked Asma about it the other night, and she gave me some very nice details and pointed me in the right direction. A little scratch-work and googling later, and ... well, it leads into some really nice stuff in QM (again). I've already got most of that post written, but before I finish it, I thought I would do a quick review of Lagrangian mechanics. (Will, this is especially for you -- I know you're going to be learning some physics this summer, and since we chatted about this the other day, I thought something a bit more formal might help.)

A quick review of Lagrangian mechanics.Collapse )
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Date: 2007-05-04 20:04
Subject: Some optics. Physics friendslist, please double-check me.
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Maxwell's equations, the wave equation, and surfaces of constant phase.Collapse )
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my journal
December 2007