Fourier bound and conditional momentum bound

Uses integration by parts, decaying boundaries, Cauchy–Schwarz and Parseval; the final step depends on phase–momentum matching.

Theory · DERIVEDEquation version 1.0.0

Based on the final manuscript · Chapter 5

ASD-WEB-QM-023

F=(x-\langle x\rangle)\psi,\quad G=(\partial_x-i\langle k\rangle)\psi,\quad2\operatorname{Re}\langle F,G\rangle=-1,\quad\Delta x\Delta k\ge\tfrac12;\quad p=\hbar k\ \Longrightarrow\ \Delta x\Delta p\ge\hbar/2

Uses integration by parts, decaying boundaries, Cauchy–Schwarz and Parseval; the final step depends on phase–momentum matching.
Chapter reference: Ch. 5 (5.3.24)–(5.3.25) · ASD-BOOK-ddbade997b45

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Ch. 5 (5.3.24)–(5.3.25)

Uses integration by parts, decaying boundaries, Cauchy–Schwarz and Parseval; the final step depends on phase–momentum matching.

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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

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QM-0accdcbe7725 · Ch. 5 (5.3.24)–(5.3.25)

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