560 reputation
1414
bio website ultracold.uchicago.edu/people
location University of Chicago, IL
age 22
visits member for 2 years, 3 months
seen Aug 13 at 15:25

University of Chicago, James Franck Institute, Undergraduate.

Imperial College London, Centre for Cold Matter, PhD Candidate.

Interests in experimental atomic/molecular physics, statistical mechanics and mathematical physics.

http://www.linkedin.com/profile/view?id=233197957&trk=tab_pro

https://www.researchgate.net/profile/Dylan_Sabulsky/


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.