Action and phase–momentum matching
The final manuscript adopts I=ℏ and total dressed-momentum matching, giving E=ℏω, P=ℏk and λ=h/P. Microscopic locking and universal normalization require a complete moving solution.
Based on the final manuscript · Chapter 5
The final manuscript adopts I=ℏ and total dressed-momentum matching, giving E=ℏω, P=ℏk and λ=h/P. Microscopic locking and universal normalization require a complete moving solution.
Chapter reference: Ch. 5 §2.3, text following (5.2.13) · ASD-BOOK-ddbade997b45
Source and ID
ASD-WEB-QM-009 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 derivationAdopted source, conditions and previous versions
Ch. 5 §2.3, text following (5.2.13)
The final manuscript adopts I=ℏ and total dressed-momentum matching, giving E=ℏω, P=ℏk and λ=h/P. Microscopic locking and universal normalization require a complete moving solution.
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: p1876 · p1879 · p1880 · p1882 · p1884 · p1900
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 §2.3, text following (5.2.13)
Dependencies
algebraEnergy and momentum from upstream dynamicsASD-WEB-QM-008Uses of this equation
Subsequent equationGroup velocity of a constant-coefficient envelopeASD-WEB-QM-010Subsequent equationFourier bound and conditional momentum boundASD-WEB-QM-023DocumentOP-QM-002 · Phase–Momentum LockingDocumentFrom Mechanical Momentum to Matter-Wave Phase