Matching input and small parameters

Ω is the slow frequency; use spectral or norm bounds, not division by Ψ at nodes. Energy matching is an input, not an algebraic output.

Theory · EFFECTIVE MODELEquation version 1.0.0

Based on the final manuscript · Chapter 5

ASD-WEB-QM-014

\hbar\omega_0\stackrel{\rm matching}{=}m_0c^2;\qquad\frac{|\Omega|}{\omega_0}\ll1,\quad\frac{ck}{\omega_0}\ll1,\quad ka_0\ll1,\quad\frac{|V|}{\hbar\omega_0}\ll1

Ω is the slow frequency; use spectral or norm bounds, not division by Ψ at nodes. Energy matching is an input, not an algebraic output.
Chapter reference: Ch. 5 §1.6, (5.1.34) · ASD-BOOK-ddbade997b45

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Ch. 5 §1.6, (5.1.34)

Ω is the slow frequency; use spectral or norm bounds, not division by Ψ at nodes. Energy matching is an input, not an algebraic output.

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: p1770 · p1803 · p1826 · p1833 · p1837 · p1841

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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QM-0accdcbe7725 · Ch. 5 §1.6, (5.1.34)

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