Fourier convention for a normalized envelope

Finite second position moment and square-integrable first weak derivative; standard deviations refer to these mathematical weights.

Theory · FOUNDATIONEquation version 1.0.0

Based on the final manuscript · Chapter 5

ASD-WEB-QM-022

\widetilde\psi(k)=\frac1{\sqrt{2\pi}}\int\psi(x)e^{-ikx}\,dx,\quad\int|\psi|^2dx=\int|\widetilde\psi|^2dk=1

Finite second position moment and square-integrable first weak derivative; standard deviations refer to these mathematical weights.
Chapter reference: Ch. 5 (5.3.23) · ASD-BOOK-ddbade997b45

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

Source and ID

ASD-WEB-QM-022 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 (5.3.23)

Finite second position moment and square-integrable first weak derivative; standard deviations refer to these mathematical weights.

Conditions retained in this adoption

Selected channel and stated initial/boundary conditions; action/energy matching retained
Continuum, slow-envelope and detector approximations kept at their respective levels

Source locators: p1967 · p1971 · p1974 · p1979 · p1980

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

QM-0accdcbe7725 · Ch. 5 (5.3.23)

DEPENDS ON

Dependencies

No preceding equation is recorded in this index. Consult the source topic for definitions, geometry and model scope.

USED BY

Uses of this equation

Discuss this page Browse all equations