Posts

The MUB Project

 I will be updating this post regarding my project work. All the orange words are links! 1) Initial report  2) MASAs and MUBs - Part 1 (edited) This report isn't complete or self contained but it is my summary of the sections of Andras Szanto's paper [here] that I found relevant to the problem. There is no original contribution from my end in either this or the previous writeup, they are only meant to clarify terminology and set the stage. Some large updates coming soon! (1 Jan 2023) Said update : I am about 11 months late to post this, but attached below is some code (in MATLAB. I am truly sorry, some array operations are just way more convenient here) I wrote to show, essentially by brute force, that all classes of weakly unextendible MASAs belong to a complementary decomposition that satisfies Szanto's criterion. See this report explaining that monstrosity of a program and some interesting findings. I hope to actually improve the speed of this program and therefore...
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Real Analysis notes (Rudin)

Chapter 1  -  Basics Chapter 2   -  Basic Topology Chapter 3  -  Sequences Chapter 4   - Continuity (in progress)
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Hoffman and Kunze Notes

Chapter 4 Chapter 5 Chapter 6 + Problems Chapter 8
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QM Notes (Shankar)

  Notes on Chapter 14 of R.Shankar's QM -- Notes on Chapters 12 and 13 of R.Shankar's QM : Part 1 Part 2  (problems mostly) Hydrogen Atom -- Notes  on Chapter 11 of R.Shankar's QM. -- Notes  on Chapter 10 of R.Shankar's QM
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Action-Angle variables for periodic systems, Adiabatic invariants

 The following is my project submission for the course PH3500 at IIT Madras. I chose to present the topic of the Action-Angle transformation and demonstrate it's elegance with regard to analysing periodic systems, and as a systematic approach to finding Adiabatic Invariants. I also illustrate a simple application of the concept of Adiabatic Invariants to approximately solve some mechanical problems.
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Transitioning to Spin : A Beginner's Perspective

This article attempts to make sense of spin from the point of view of a beginner. It tries to make this transition a bit smoother and better motivated. Kindly click the following  link (edited) to read it.
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A Game of "Society"

Here I have attached a document presenting my solution to the following problem, which was asked in  IISc  Bangalore’s  2020  Pravega  event  :  "Gaussian Gambit". Specifically, the last  question  of  Problem Set 1  :  "A group  of  n  students  in  a  classroom are playing  a game of  ‘Society’.  Each student has  some friends  (possibly  none), and  friendship  is  mutual.  Every student begins  with  an  integral  amount of  dollars  (possibly  negative). A  move consists  of  some student giving  $1  to each  of  their  friends.  We say  that the game is  fair  if  it is  possible to  transform  the original  distribution  of  money  into any  other  arbitrary  one with  the same amount ...
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