EQUATION REGISTRY

Schrödinger-type effective envelope

Drop the second envelope time derivative and use the matching input; the familiar scalar form additionally takes B=I and no source.

Theory · EFFECTIVE MODELEquation version 1.0.0

Based on the final manuscript · Chapter 5

ASD-WEB-QM-015
iℏ∂tΨ=−ℏ22m0∂i(Bij∂jΨ)+VΨ+SSch,SSch=−ℏ2ω0S0i\hbar\partial_t\Psi=-\frac{\hbar^2}{2m_0}\partial_i(B_{ij}\partial_j\Psi)+V\Psi+S_{\rm Sch},\qquad S_{\rm Sch}=-\frac{\hbar}{2\omega_0}S_0

Drop the second envelope time derivative and use the matching input; the familiar scalar form additionally takes B=I and no source.
Chapter reference: Ch. 5 (5.1.35) · ASD-BOOK-ddbade997b45

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Adopted source, conditions and previous versions

Ch. 5 (5.1.35)

Drop the second envelope time derivative and use the matching input; the familiar scalar form additionally takes B=I and no source.

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 (5.1.35)

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