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Precise calculation of the transmission coefficient of a potential barrier. Study of the error in the B K W approximation; Calcul exact du coefficient de transmission d'une barriere de potentiel. Etude de l'erreur de l'approximation B K W

Abstract

Following on to work started in a previous report, the author carries out in the case of few examples, the calculation of the transmission coefficient T using accurate methods. He then deduces from this the error in the B K W method. The calculations are carried out for values of T ranging down to 10{sup -200}. The use of modern computers makes it possible to obtain values of T to eight decimal places in a few seconds and the practical advantage of the B K W approximation appears therefore considerably reduced. The author gives also a method which may be used for an exact calculation of the energy levels of a potential well. (author) [French] Poursuivant une etude commencee dans une note anterieure, l'auteur effectue, sur quelques exemples, le calcul du coefficient de transmission T par des methodes exactes. Il en deduit ensuite l'erreur de la methode B K W. Les calculs sont faits pour des valeurs de T allant jusqu'a 10{sup -200}. L'utilisation des machines a calculer modernes permettant d'obtenir en quelques secondes, la valeur de T avec 8 decimales exactes, l'interet pratique de l'approximation B K W semble considerablement diminue. L'auteur indique egalement une methode qui peut servir  More>>
Authors:
Jamet, P [1] 
  1. Commissariat a l'Energie Atomique, Saclay (France). Centre d'Etudes Nucleaires
Publication Date:
Jul 01, 1964
Product Type:
Technical Report
Report Number:
CEA-R-2626
Resource Relation:
Other Information: 4 refs
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCULATION METHODS; COMPUTER CALCULATIONS; CONVERGENCE; INTEGRAL CALCULUS; POTENTIALS; SCHROEDINGER EQUATION; WKB APPROXIMATION
OSTI ID:
20650643
Research Organizations:
CEA Saclay, 91 - Gif-sur-Yvette (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR05R2626090256
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
35 pages
Announcement Date:
Nov 23, 2005

Citation Formats

Jamet, P. Precise calculation of the transmission coefficient of a potential barrier. Study of the error in the B K W approximation; Calcul exact du coefficient de transmission d'une barriere de potentiel. Etude de l'erreur de l'approximation B K W. France: N. p., 1964. Web.
Jamet, P. Precise calculation of the transmission coefficient of a potential barrier. Study of the error in the B K W approximation; Calcul exact du coefficient de transmission d'une barriere de potentiel. Etude de l'erreur de l'approximation B K W. France.
Jamet, P. 1964. "Precise calculation of the transmission coefficient of a potential barrier. Study of the error in the B K W approximation; Calcul exact du coefficient de transmission d'une barriere de potentiel. Etude de l'erreur de l'approximation B K W." France.
@misc{etde_20650643,
title = {Precise calculation of the transmission coefficient of a potential barrier. Study of the error in the B K W approximation; Calcul exact du coefficient de transmission d'une barriere de potentiel. Etude de l'erreur de l'approximation B K W}
author = {Jamet, P}
abstractNote = {Following on to work started in a previous report, the author carries out in the case of few examples, the calculation of the transmission coefficient T using accurate methods. He then deduces from this the error in the B K W method. The calculations are carried out for values of T ranging down to 10{sup -200}. The use of modern computers makes it possible to obtain values of T to eight decimal places in a few seconds and the practical advantage of the B K W approximation appears therefore considerably reduced. The author gives also a method which may be used for an exact calculation of the energy levels of a potential well. (author) [French] Poursuivant une etude commencee dans une note anterieure, l'auteur effectue, sur quelques exemples, le calcul du coefficient de transmission T par des methodes exactes. Il en deduit ensuite l'erreur de la methode B K W. Les calculs sont faits pour des valeurs de T allant jusqu'a 10{sup -200}. L'utilisation des machines a calculer modernes permettant d'obtenir en quelques secondes, la valeur de T avec 8 decimales exactes, l'interet pratique de l'approximation B K W semble considerablement diminue. L'auteur indique egalement une methode qui peut servir a calculer exactement les niveaux d'energie d'un puits de potentiel. (auteur)}
place = {France}
year = {1964}
month = {Jul}
}