Hello! This is Kelanu's Website
Table of contents
- About Me
- Interesting Formulas
- Publications and Awards
- Art and Graphs
- Climbing, Snowboarding and Slacklining
- Music
- Solutions to Selected Problems
- Quantum Information and Compution Wiki

Cool People (Who Also Have A Website)
UCLA | Mel | Carter | Seth | Eric | Daniel | Liyu | Nathan | Srinjina | Kyle | Hunter | Logan | Brian | Ky |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Lumitron | Christine | Mauricio | |||||||||||
James | Joy | Jason | |||||||||||
Co-op | Silvia | Eli | |||||||||||
Other | Aaron |
People I Do Not Know But I Think Are Cool
- Isreal Gelfand
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.
- Paul Erdos
- Alexander Grothendieck
Below is a picture of Grothendieck with his students in North Vietnam in 1967.
About Me
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:
- Physics 115C: Quantum Mechanics
- Physics 180Q: Quantum Optics Laboratory
- ECE 279AS: Special Topics in Physical and Wave Electronics: Physics of Quantum Information and Computation
- ECE 271: Classical Laser Theory
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.
Interesting Formulas
Formulas Involving Displacement Operators
The following formulas are useful when dealing with displacement operators.
This one I found on Stack Exchange but I forgot where and only have the original link.
This one is courtesy of Ryan.
Consider the following expansions
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.
Perturbation Theory
The first order correction to an anharmonic oscillator requires evaluating
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.
Riesz Representation Theorem
Gelfand Triple
LuaLaTeX
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.
Solutions to Selected Problems
Quantum Computing
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.
"Ramsey" spectroscopy with a QHO?!
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 $\omega=2\pi$.