Envelope boundary problem for a rectangular barrier

0<E<V₀, equal masses, B=I and barrier width a; ψ and ψ′ are continuous across finite steps.

Theory · EFFECTIVE MODELEquation version 1.0.0

Based on the final manuscript · Chapter 5

-\frac{\hbar^2}{2m_0}\psi''+V\psi=E\psi,\quad k=\sqrt{2m_0E}/\hbar,\quad\kappa=\sqrt{2m_0(V_0-E)}/\hbar,\quad\psi_{\rm II}=Ae^{\kappa x}+Be^{-\kappa x}

0<E<V₀, equal masses, B=I and barrier width a; ψ and ψ′ are continuous across finite steps.
Chapter reference: Ch. 5 (5.3.28)–(5.3.31) · ASD-BOOK-ddbade997b45

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

Source and ID

ASD-WEB-QM-030 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 (5.3.28)–(5.3.31)

0<E<V₀, equal masses, B=I and barrier width a; ψ and ψ′ are continuous across finite steps.

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: p1984 · p1993 · p1995 · p1997 · p2000 · p2008 · p2012

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 (5.3.28)–(5.3.31)

DEPENDS ON

Dependencies

USED BY

Uses of this equation

Discuss this page Browse all equations