Dylan Sabulsky
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 May 29 comment Deriving the Angular Momentum Commutator Relations by using $\epsilon_{ijk}$ Identities Argue that (ijk) -> (xyz) and that the same answer holds for (jki) -> (yzx) etc. Changing the indices doesn't change the solution, for any permutation. You could write it out, explaining, or you could actually show the permutations are the same simply. Feb 21 comment Supplements for Kittel's Solid State Physics? Condensed Matter Physics by Marder may also interest you, but I think his section on crystallography is tiny. Feb 17 comment Rewriting Creation and Annihilation Operators Thanks so much for your help KDN. Awesome Feb 17 comment Rewriting Creation and Annihilation Operators of course, it is 1. $$[a,a^{\dagger}]=1$$ Feb 17 comment Rewriting Creation and Annihilation Operators I'm afraid it doesn't. Feb 17 comment Rewriting Creation and Annihilation Operators Great call, hadn't even considered it in my foolishness. $$[p_{i},r_{j}]=[p_{i},r_{j}]=-i\hbar \delta_{ij}$$ $$[R_{i},\pi_{j}]=0$$ $$[\pi_{i},\pi_{j}]=-i \epsilon_{ij} m \hbar \omega_{c}=-i \epsilon_{ij} \frac{\hbar^{2}}{l_{b}^{2}}$$ $$[R_{i},R_{j}]=i \epsilon_{ij} l_{b}^{2}$$ $$[\rho_{i},\rho_{j}]=-i \epsilon_{ij} l_{b}^{2}$$ $$[\rho_{i},\pi_{j}]=i \hbar \delta_{ij}$$ $$[p_{i},\pi_{j}]=-i \hbar \frac{e}{c} \frac{\partial A_{j}}{\partial r_{i}}$$ $$[R_{i},r_{j}]=i \epsilon_{ij} l_{b}^{2}$$ $$[\rho_{i},r_{j}]=-i \epsilon_{ij} l_{b}^{2}$$ Feb 17 comment Rewriting Creation and Annihilation Operators For context, I am studying the quantum Hall Effect, integer and fractional, and this came up in my instructors online notes. I am unsure why you would rewrite this, and further what is the best way to approach it. To expand on my idea, I was thinking to expand $\pi$ to $\vec{\pi}=m\vec{v}=\vec{p}-\frac{q}{c}\vec{A}$ and perhaps try from there. Feb 12 comment Projectile motion, canon vs cliff Working on this now. Also, the velocity of the ball at the top of the cliff is zero because if it were not, it would go higher than 85m; the question tells you it just reaches the top. Feb 12 comment Additional mass of block on inclined plane Thanks for showing your work Justin. In your original work I believe you did not cancel a factor of $g$ and did not evaluate the sine properly. The cloth is a ruse to get you to ignore friction effects. Friction problems of this caliber will usually tell you how to obtain friction or just give you a coefficient of friction. Feb 12 comment Additional mass of block on inclined plane Admittedly, bear is pretty good. Feb 12 comment Additional mass of block on inclined plane Ok cool, one sec Feb 12 comment Additional mass of block on inclined plane Fair enough. Can you tell me anything else? Like distances, heights, etc? I can follow your work I think but I dont want to assume values. For example, what is theta? Feb 12 comment Additional mass of block on inclined plane Brother, theta is spelled wrong. Further, friction does not alter the fundamental components of mass and the forces of gravity Jan 28 comment Question about Classical Transport Theory awesome, thanks Joe! Jan 27 comment Question about Classical Transport Theory You are correct in both regard. The B field is indeed assumed directed along $\hat{z}$ and the $\omega_{c}$ is the cyclotron frequency. Dec 8 comment Is there a small enough planet or asteroid you can orbit by jumping? THIS PICTURE. +1 Dec 7 comment Two photons of different frequencies collide to create electron and positron fair enough! +1 Dec 7 comment Origin of exchage interactions Thank you, I appreciate it! This is great. Dec 7 comment Two photons of different frequencies collide to create electron and positron How does this help to determine what $f$ is? It is still indeterminate through what you described, right? Dec 7 comment Unrolling electrolytic capacitors It is mostly for isolation purposes. Also it keeps the liquid in pretty well. If it is electrolytic, it also has a cross cut into the top. It the capacitor is overloaded, it will bulge out before blowing spectacularly. The aluminum casing is strong enough to usually hold from blowing in a case of overload.