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Consider the orbital angular momentum in QM, labeled by $L$ ($mathbf{L}=mathbf{r}timesmathbf{p}$). In spherical coordinate, the operator can be expressed as:begin{equation*}left{begin{aligned} L_x&=frac{hbar}{mathrm{i}}left(-sinphifrac{partial}{partial theta}-cosphicotthetafrac{partial}{partial phi}right)\...
Asked on 12/31/2021
2 answerThe FLRW metric, in the case of positive scalar curvature, is: $ds^2 =- c^2 dt^2+a(t)^2left(dw^2+sin^{2}w(dtheta^2+sin^2theta dphi^2)right)$. The Birkhoff’s theorem states that "any spherically symmetric solution of the vacuum field...
Asked on 12/31/2021
1 answerHere, the natural length of the string is $l_o$, and pulling the string up by $x$ increases its...
Asked on 12/31/2021
1 answerI'm aware of the common misunderstanding about action and reaction canceling each other; they don't because they don't act on the same object. This is about a more subtle...
Asked on 12/31/2021
2 answerThis is a thought experiment where I have made a "C" shaped hole inside diamond. The refractive index $(mu)$ of diamond is 2.45....
Asked on 12/31/2021
4 answerEquation of principal angles: $$tan 2theta_p=frac{2tau_{xy}}{sigma_x-sigma_y}$$ Equation of principal stresses:$$sigma_{max}, sigma_{min} = {sigma_{xx} + sigma_{yy} over 2} pmsqrt{ left( {sigma_{xx} - sigma_{yy} over 2} right)^2 +...
Asked on 12/31/2021
1 answerI studied a sciences of climate change module with the OU a while ago, I'm half remembering something that's bugging me and wonder whether any could help provide some clarification?...
Asked on 12/29/2021
1 answerFor the purpose of this question, I'm making the assumption that atoms are fixed in space, and as such possess no vibrational degrees of freedom. A crystalline solid is a...
Asked on 12/29/2021
1 answerCan anyone figure out what is wrong with this perpetual motion machine? What part of it violates physics? I found it on a website a while ago, and I couldn't...
Asked on 12/29/2021
4 answerI read here that a black hole with a mass of the observable universe, $M=8.8times10^{52}kg$, would have a Schwarzschild radius of $r_s=13.7$ billion lightyears. I immediately...
Asked on 12/29/2021
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