| UCLA | Mel | Carter | Seth | Eric | Daniel | Liyu | Nathan | Srinjina | Kyle | Hunter | Logan | Brian | Ky |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Lumitron | Christine | Mauricio | |||||||||||
| James | Joy | Jason | |||||||||||
| Other | Aaron |
Anyone with an interest in mathematical physics or AQFT has no doubt come across the name Gelfand of the famous "Gelfand Triple/Sandwich" or GNS construction. I found, after reading more about him, that he was also influential in molecular biology, ran a correspondence school for those who didn't have access to a university, and believed in animal rights and was a vegetarian then vegan towards the end of his life.
Below is a picture of Grothendieck with his students in North Vietnam in 1967.
My name is Kelanu. I study physics and mathematics at UCLA. I was previously an engineering intern at Lumitron Technologies from June 2021 to April 2024. I now work for Professor Saltzberg at UCLA as an undergraduate research assistant.
I am currently taking:
I have a spreadsheet of every TV show and movie I have or plan on seeing; feel free to add comments.
If you want to contact me my email is kelanucr at g dot ucla dot edu or kranganath at physics dot ucla dot edu.
Once a month for the past four years I make a collaborative playlist, previously this has been on Spotify, this year I am trying YouTube Music. If you would like to add to the playlist this is the link
I have a YouTube channel.
The following formulas are useful when dealing with displacement operators.
$$\langle \psi_m | \mathcal{D}(\alpha) | \psi_n \rangle = \sqrt{\frac{m!}{n!}}(-\alpha^\ast)^{n-m}\exp(-\frac{1}{2}|\alpha|^2)L_m^{n-m}(|\alpha|^2)$$
This one I found on Stack Exchange but I forgot where and only have the original link.
$$\langle \psi_m | \psi_n \rangle = $$
This one is courtesy of Ryan.
Consider the following expansions
$$\mathcal{D}(1) = e^{a-a^\dagger}=e^{\gamma \hat{p}} = \sum_k \frac{\gamma^k}{k!}\hat{p}^k$$
$$\mathcal{D}(i) = e^{ia+ia^\dagger}=e^{\lambda \hat{x}} = \sum_k \frac{\lambda^k}{k!}\hat{x}^k$$
We know however, that a displacement by a purely real alpha is kick in position and a purely complex displacement is a kick in momentum. We see then that displacements in momentum are equivalent to position operators and vice versa.
The first order correction to an anharmonic oscillator requires evaluating
$$\langle \psi_n | x^k | \psi_j \rangle$$
First we notice that if we expand $x^k = \gamma^k (a + a ^\dagger)^k$ then we can evaluate this by hand by drawing trees. It would be nice if we could instead have a formula for this.
$$\frac{k!\sqrt{n!j!}}{\sqrt{2^k}}\sum_{m=0}^{\left \lfloor{\frac{k}{2}}\right \rfloor}\frac{1}{2^m m!}\frac{1}{(s-n)!(s-j)!(s-k+2m)!}$$
I am a big fan of LuaLaTeX, I've been using it to compile my LaTeX documents for close to two years now. In that time I've developed a set of scripts and enviroments that transform psuedo-code into well defined LaTeX macros for ease of use -nothing takes you out of the flow quite like aa curly bracket am I right fellas.
There are still some big bugs to work out before I can release it, but when I do I'll put a link here.
These are selected problems from Physics 245 at UCLA with Professor Hudson. A lot of the problems are computational and use a package called QuTip. I've selected some of the non-QuTip problems that I think have an interesting solution.
Suppose at $t=0$ a vacuum state is displaced by a displacement operator with $\alpha = 1$. Then after a variable time $t_w$ a second displacement operator with $\alpha = -1$ is applied. Plot the probability of being in the vacuum state as a function of $t_w$, assume that $m=1kg$ and $\omega=2\pi$.
Professor Shankar's textbook "Principles of Quantum Mechanics" is a classic in graduate level quantum mechanics along side Sakurai. Recently (2017) he published another banger, "Quantum Field Theory And Condensed Matter An Introduction." So here are some solutions to the exercises in the first chapter.
This graph shows some simple radar simulations.
This one is a dirac comb.
This one is some polar art.
This one is more polar art.
This one uses the Lambert W function to model an emmiter follower circuit.
I started climbing in 2022. I quickly found that in the absence of rocks there were routes scattered around campus. There used to be a Mountain Project for UCLA, the routes and images were taken down sometime in 2023. I saved most of them and re-uploaded the routes and added several new ones to a Google Map.
I like snowboarding.
