Nonlocal density energy

k≠0; real-space kinetic energy contains the inverse Laplacian.

Theory · DERIVEDEquation version 1.0.0

Based on the final manuscript · Chapters 4 and 5

\mathbf u_L(\mathbf k)=\frac{i\mathbf k}{k^2}\sigma,\quad E_L=\frac{Z_L}{2}\int\frac{d^3k}{(2\pi)^3}\left[\frac{|\partial_t\sigma|^2}{k^2}+c^2|\sigma|^2\right]

k≠0; real-space kinetic energy contains the inverse Laplacian.
Chapter reference: Ch. 5 (5.4.8)–(5.4.10) · ASD-BOOK-ddbade997b45

Assumptions and derivation Registry and dependencies Research this equation Discuss this equation

Source and ID

ASD-WEB-SD-014 is the stable website equation ID. It retains existing links and does not replace the manuscript reference. Use the copy button to obtain LaTeX.

Return to premises and derivation

Adopted source, conditions and previous versions

Ch. 5 (5.4.8)–(5.4.10)

Registered formula checked individually against the final manuscript; The mathematical content agrees; the existing expression and its derivation conditions are retained.

Conditions retained in this adoption

k≠0; real-space kinetic energy contains the inverse Laplacian.

Source locators: p2035–2040

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

Download source identity manifest

The manifest identifies the source; it is not the complete manuscript. Adopting this source does not upgrade evidence or grant a new licence.

Previous source, retained as history

SD-51779505a476 · Ch. 5 (5.4.8)–(5.4.10)

DEPENDS ON

Dependencies

USED BY

Uses of this equation

Discuss this page Browse all equations