Langer correction

Langer correction

The Langer correction is a correction when WKB approximation method is applied to three-dimensional problems with spherical symmetry.

When applying WKB approximation method to the radial Schrödinger equation: -frac{hbar^2}{2 m} frac{d^2 R(r)}{dr^2} + [E-V_{eff}(r)] R(r) = 0 where the effective potential is given by:V_{ extrm{eff(r)=V(r)-frac{l(l+1)hbar^2}{2mr^2}the eigenenergies and the wave function behaviour obtained are different from real solution.

In 1937, R.E. Langer suggested a correction

:l(l+1) ightarrow left(l+frac{1}{2} ight)^2which is known as Langer correction. This is equivalent to inserting a 1/4 constant factor whenever l(l+1) appears. Heuristically, it is said that this factor arises because the range of the radial Schrödinger equation is restricted from 0 to infinity, as opposed to the entire real line.

By such a changing of constant term in the effective potential, the results obtained by WKB approximation reproduces the exact spectrum for many potentials.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Vibration Correction — Als Bildstabilisierung bezeichnet man in der Fototechnik Verfahren zur Vermeidung von Verwacklungsunschärfe. Inhaltsverzeichnis 1 Grundlagen 2 Funktionsprinzipien 2.1 Optische Bildstabilisierung 2.1.1 Implementierung im Objektiv …   Deutsch Wikipedia

  • WKB approximation — In physics, the WKB (Wentzel–Kramers–Brillouin) approximation, also known as WKBJ (Wentzel–Kramers–Brillouin–Jeffreys) approximation, is the most familiar example of a semiclassical calculation in quantum mechanics in which the wavefunction is… …   Wikipedia

  • Aproximación WKB — En Física, la aproximación WKB es el ejemplo más familiar de un cálculo semi clásico (ver antigua teoría cuántica) en el cual la función de onda es redactada como una función exponencial, semiclásicamente expandida, y entonces o la amplitud o la… …   Wikipedia Español

  • MESSENGER — bei den Startvorbereitungen NSSDC ID 2004 030A Missionsziel Merkur Auftraggeber NASA …   Deutsch Wikipedia

  • Messenger (Raumsonde) — Zeichnerische Darstellung von MESSENGER in der Nähe von Merkur MESSENGER bei den Startvorbereitungen MESSENGER (MErcury Surface, Space ENvironment, GEochemistry and Ranging) ist e …   Deutsch Wikipedia

  • 1,1,1-Trichloroethane — Not to be confused with 1,1,1 Trifluoroethane. 1,1,1 Trichloroethane …   Wikipedia

  • ALR-94 — Lockheed Martin F 22 Raptor …   Deutsch Wikipedia

  • AN/ALR-94 — Lockheed Martin F 22 Raptor …   Deutsch Wikipedia

  • AN/APG-77 — Lockheed Martin F 22 Raptor …   Deutsch Wikipedia

  • APG-77 — Lockheed Martin F 22 Raptor …   Deutsch Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”