This is an ongoing project to digitize, organize, and expand on all of my notes covering topics in mathematics and physics. The goal that drove the creation of this site is the desire to archive the body of material I've been exposed to through research and coursework. By doing this I want to solidify my understanding for a wide variety of topics I care about by writing about them and also by experimenting with ways to connect them in such a way that new insights may emerge. The topics represented here are written from the perspective of someone who wants to understand quantum mechanics and its underlying mathematical principles in order to apply these principles in topics tied to quantum materials, quantum optics, quantum information, and quantum foundations. You may jump right into the topics I cover on this site [here](Welcome%20to%20The%20Quantum%20Well!.md#Indices) or read about some of my meta-commentary on what exactly I'm doing [here]( and [here]( In addition, I believe that a large body of inter-related notes leads to the creation of blocks of text and equations that may make it in drafts of publishable work. This site is hosted on [Obsidian Publish]( and looks the way it does because of the hard work by the team at [Obsidian]( as well as by the contribution by [Gordon Peterson (deathau)]( in developing and sharing with the community the theme, _[Notation](, which I have tweaked to fit my needs and tastes. # Indices This site is organized around a hierarchy of indices and sub-indices of interconnected topics. Some of the top level indices are listed below and everything is listed on the left sidebar. The intention is for each index and sub-index to include a bibliography of textbooks, articles, and lecture notes I've consulted in order to create this site. In addition, the index pages will include both introductory remarks to contextualize the topics listed in them as well as brief overviews of prerequisite concepts. * [🗄️Electromagnetisim](Electromagnetism%20(index).md) * [🗃️Optics](Optics%20(Index).md) * [🗃️Experimental tools in optics](Experimental%20tools%20in%20optics%20(index).md) * [🗃️Physical examples in optics](Physical%20Examples,%20Optics%20(index).md) * [🗄️Mathematical foundations](Mathematical%20Foundations%20(Index)) * [🗃️Abstract algebra](Algebra%20(index).md) * [🗃️Lie groups, algebras, and representations](Lie%20groups,%20algebras,%20and%20representations%20(Index).md) * [🗃️Linear algebra and matrix theory](Linear%20Algebra%20and%20Matrix%20Theory%20(index).md) * [🗃️Tensors and multilinear algebra](Tensors%20and%20Multilinear%20Algebra%20(index).md) * [🗃️Analysis](Analysis%20(index).md) * [🗃️Complex analysis](Complex%20analysis%20(index).md) * [🗃️Differential equations](Differential%20equations%20(index).md) * [🗃️Fourier analysis](Fourier%20analysis%20(Index).md) * [🗃️Functional analysis](Functional%20analysis%20(index).md) * [🗃️Vector analysis](Vector%20analysis%20(index).md) * [🗃️Geometry](Geometry%20(index).md) * [🗃️Differential geometry](Differential%20geometry%20(index).md) * [🗃️Topology](Topology%20(index).md) * [🗃️Numbers](Numbers%20(index).md) * [🗃️Sets](Sets%20(index).md) * [🗃️Statistics and probability](Statistics%20and%20Probability%20(index).md) * [🗃️ Probability distributions](Probability%20distributions%20(index).md) * [🗄️Mechanics](Mechanics%20(index).md) * [🗃️Mechanical models](Physical%20Examples,%20Mechanics%20(index).md) * [🗃️Special relativity](Special%20Relativity%20(Index).md) * [🗃️Wave mechanics](Wave%20Mechanics%20(index).md) * [🗄️Quantum mechanics](Quantum%20Mechanics%20(index).md) * [🗃️Atomic physics](Atomic%20Physics%20(Index).md) * [🗃️Elementary particles](Elementary%20Particles%20(index)) * [🗃️Experiments in quantum mechanics](Experiments%20in%20Quantum%20Mechanics%20(index)) * [🗃️Interpretations and foundations of quantum mechanics](Interpretations%20and%20Foundations%20of%20Quantum%20Mechanics%20(index).md) * [🗃️Multi-particle quantum systems](Multi-particle%20quantum%20systems%20(index)) * [🗃️Quantum dynamics](Quantum%20Dynamics%20(index)) * [🗃️Quantum field theory](Quantum%20Field%20Theory%20(Index).md) * [🗃️Quantum mechanics accounting for relativity](Relativistic%20Quantum%20Mechanics%20(index).md) * [🗃️Quantum information](Quantum%20Information%20(index)) * [🗃️Quantum measurement](quantum%20measurement%20(index)) * [🗃️Quantum optics](Quantum%20Optics%20(index).md) * [🗃️Stationary quantum systems](Stationary%20Quantum%20Systems%20(Index).md) * [🗄️ 🚧🏗️ Thermodynamics and statistical physics](Thermodynamics%20and%20Statistical%20Physics%20(Index).md)^[Note many of the pages indexed in this section will remain unpublished for the time being since they contain copyrighted figures that are sourced from a pre-print textbook in statistical physics that is not publicly available. In addition, these figures, as they appear in the pre-print are also taken from different sources without attribution for the time being. This leaves me with three options: wait for the textbook to be published, ask for permission from the author along with requesting that they send me a bibliography of their sources, or make my own figures. That last option is the best one but it takes time.] ## Course Notes I'll be creating additional indices in order to categorize sets of notes as "courses." These will simply order and organize topics and exercises in units that follow a particular semester-length course. These courses will initially be based of graduate level courses I've taken at Ludwig Maximilian University of Munich along with my own insights and additional readings. What I would consider "Exercises" are in subsections where some mathematical statement is proven, or in anything tagged with # PhysicalExamples. This is a planned feature that won't be expanded for quite a while. Look for them on the side-bar. ## Uncategorized Notes There are uncategorized notes listed on the bottom of the side bar. These will eventually be moved to the main indices as time goes on. However, in order to save time while reviewing a topic so I can avoid becoming a full-time librarian, quick notes, new course notes, and rough drafts of notes will be added here. # The Graph View! Below is a screenshot of the full graph view as it appears on my desktop version of this site. The yellow dots represent figures, miscellaneous files, or files corresponding to cited literature on this site, the gray nodes are all either the topics or indices listed on the sidebar and are stored as .md files, and the green nodes are tags. ![](Pasted%20image%2020230205012743.png) As of February 5th 2023 there are a total of 1427 files represented in the above image. 978 of these files are notes entries. 116 of these files are mostly unpublished notes on statistical physics and thermodynamics. The number of nodes is actually slightly understated by this number since the tags aren't stored as files. An interactive global graph view is now visible if you click on the "global graph" button on the mini interactive graph view window. # Disclaimer Be aware that this is very much a work in progress. Many of these notes are incomplete or entirely empty! And as the content map grows, the number of topics I'll want to revisit and expand on later will continue to grow (adding even more empty notes and dead links). Thus, this site will never look complete. If you see any mistakes here, don't hesitate to point them out. I am continually proofreading and revisiting topics. However, I am one person writing about things on my own and _there are_ mistakes on here that go beyond mere typos. One of the problems is that while I may be somewhat qualified to write at length about physics, I'm not a mathematician and I've never taken any courses in abstract algebra or analysis either, but I spend a lot of time writing about those topics anyway out of a desire to master them. # Contact I'm open to suggestions, criticism, or questions about what I have written. Let me know also if you've derived any benefit from these notes or would want to contribute. I would appreciate all the help I can get! Please send all feedback to: [email protected] ^305618 %%The written content on this site is entirely authored by me, Boris. Follow me on [Twitter]( (I mostly tweet about things unrelated to this project.) I'm also on Mastodon under the same handle: ^a5816a%% %%You may also reach me on my Discord channel at ^71ab37 %% # Using my notes I want all knowledge to be free forever! I want to share what I know, collaborate, and learn. However, don't take credit for what I have here, or distribute what I make without attribution. Therefore the following license applies to everything I write and all figures and drawings that I make myself or in collaboration with anyone else: ^6a9c37 <a rel="license" href=""><img alt="Creative Commons License" style="border-width:0" src="" /></a><br />This work is licensed under a <a rel="license" href="">Creative Commons Attribution 4.0 International License</a>. ^b7a7d7 All figures and tables of contents that are from textbook sources belong to their original copyright holder. ^e00c28