Built on Facts

Disclaimer for casual readers: I write posts which vary wildly in technical difficulty, this one is a little more mathematical than most. Don’t let it scare you off! Even if you’re a little lost, it’s good to have seen it.
The various worked problems I’ve been doing recently have mostly been on the intro [...]

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Next semester I’m taking the graduate classical mechanics class, and so I’m trying to spend a little time this summer brushing up on my old undergraduate mechanics. It’s been about three years since I’ve had to do much of it, and I’ve dug out my old books and am working on some problems. [...]

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Vis consili expers mole ruit sua.
- Quintus Horatius Flaccus
The words of Horace above attain a spare and austere beauty in Latin, but the meaning is carried equally well in English. Force without wisdom falls of its own weight. Two different sets of words carry his millenia-old thoughts to the present time. There [...]

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In a vacuum, the speed of light is a universal constant: 299,792,458 m/s exactly. For light traveling through a substance like water or glass the speed is lower. The light hasn’t actually slowed down. Instead, the interaction with each successive atom in the material takes a little bit of time and so [...]

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Quantum mechanics is difficult. “Yeah, yeah,” you say, “tell me something new”. But it’s not only a bit tricky to learn. Mathematically there’s simply not a way to get exact solutions to all of the problems we face. They just don’t exist in a nice short closed form. But we’d [...]

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In honor of the NBA playoffs, how about some quantum mechanics? Ok, maybe it’s a stretch! But let’s say we have a particle bouncing on a hard surface. We can model this by defining a floor at x = 0. For x > 0, the potential V(x) = mgx. For [...]

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