#notes

6 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...

maths fluid-dynamics notes transcription ai-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 $ℌ = 𝐿^{2} (𝐵, d 𝜇; ℂ)$ . Local finiteness implies that...

maths functional-analysis self-adjointness notes rough

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 $0 \leq 𝛼 < 1$ . We say that an operator $𝐵$ defined on $𝐷 (𝐴)$ is $𝐴$ -bounded with relative bound $𝛼$ if...

maths functional-analysis self-adjointness notes rough

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...

maths functional-analysis notes rough

May 1, 2026

Notes on Lewin Ch1: Introduction to Quantum Mechanics

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

maths quantum-mechanics notes rough hamiltonian-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...

maths notes quantum-mechanics sobolev-spaces functional-analysis rough