#notes6 posts

June 2, 2026

Navier–Stokes Existence or Breakdown

This is an AI-generated survey distilled from a talk by Javier Gómez-Serrano , lightly edited but not independently checked line by line. Treat it as...

mathsfluid-dynamicsnotestranscriptionai-assisted

May 19, 2026

Notes on Lewin Ch4: Spectral Theorem and Functional Calculus

1 Multiplication Operators Let $𝐵\subset {ℝ}^{𝑑}$ be Borel, and let $𝜇$ be a locally finite Borel measure on $𝐵$. We set $ℌ={𝐿}^2(𝐵,d𝜇;ℂ)$. Local finiteness implies that...

mathsfunctional-analysisself-adjointnessnotesrough

May 15, 2026

Notes on Lewin Ch3: Self-adjointness Criteria: Rellich, Kato and Friedrichs

Rellich–Kato Let $(𝐴,𝐷(𝐴))$ be a self-adjoint operator and $0\le 𝛼<1$. We say that an operator $𝐵$ defined on $𝐷(𝐴)$ is $𝐴$-bounded with relative bound $𝛼$ if...

mathsfunctional-analysisself-adjointnessnotesrough

May 7, 2026

Notes on Lewin Ch2: Self-adjointness

Let $ℌ$ be a separable Hilbert space over $ℂ$. Graphs Definition: the graph of an operator $(𝐴,𝐷(𝐴))$ is the vector subpsace of $ℌ\times ℌ$ given by...

mathsfunctional-analysisnotesrough

May 1, 2026

Notes on Lewin Ch1: Introduction to Quantum Mechanics

Important notation $⟨𝑓\text{,}𝑔⟩≔\int \overline{𝑓}𝑔$, so it is antilinear in the first index and linear in the second. $⟨𝐴⟩≔⟨𝜓\text{,}𝐴𝜓⟩$. Also - as I am playing on my...

mathsquantum-mechanicsnotesroughhamiltonian-operators

April 24, 2024

Notes on Lewin Appendix

Appendix A: Sobolev Spaces Definition Definition of ${𝑊}^{𝑘,𝑝}$ is given, and the Meyer-Serrin theorem $𝐻=𝑊$ is stated without proof. Sobolev spaces on the interval Considering...

mathsnotesquantum-mechanicssobolev-spacesfunctional-analysisrough