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Edited by The Cellar Door:
4/2/2016 3:36:27 AM
7
Prove d⟨p⟩/dt =⟨-∂V/∂x⟩, given that d⟨p⟩/dt = -iħ∫∂/∂t (ψ*∂ψ/∂x) dx and ∂^2ψ/∂x∂t=∂^2ψ/∂t∂x
Bonus points if you can tell me who's theorem this is without google.
English
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I'm in calc right now and when I show people some equations they say all they see is a bunch of hieroglyphs. Well, that's exactly what I see right now. A bunch of hieroglyphs. Definitely not gonna take physics...
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Edited by The Cellar Door: 4/2/2016 8:41:17 PMIt's really not that bad. Anything with a d before it signifies that that's a derivative. Anything with a ∂ is a partial derivative. ψ is wave function. ħ is the reduced Planck constant. -i is denoting a complex number due to how it is derived. After understanding that it's just having a good grasp of calculus and a conceptual understanding of quantum mechanics.
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Huh. After almost a year of doing calc, it makes a lot more sense. At first I saw everything as being really complex and hard to solve, but now everything is just equations and simple algebra, with some overlapping concepts like derivatives. Is it the same way for physics?
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Yes, completely. As for Newton's laws of motion; Position is the second derivative of acceleration, and the first derivative of velocity. Acceleration is the second integral of position, and the first integral of velocity. You get more complexities when you're able to use partial derivatives to use variables with respect to other variables, which is why you'll tend to see the partial derivative sign a lot on higher level physics.
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What is this seriously lol. I assume it's in your physics book?
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Edited by The Cellar Door: 4/2/2016 4:44:11 AMWell besides that, it's a pretty well known theorem connecting classical physics and quantum mechanics, at least to anyone who's studied quantum mechanics before, I'd imagine they'd know this. It mathematically proves what Neils Bohr said, which is basically that in the upper limits of quantum mechanics, expectations should equal what classical physics says they should. This particular equation proves that for Newton's laws of motion.
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Pretty cool stuff you are doing there.
