Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T13:34:32.866Z Has data issue: false hasContentIssue false
  • English
  • Français

The use of the Airy functions in a potential barrier problem

Published online by Cambridge University Press:  24 October 2008

Bertha Jeffreys
Bertha Jeffreys
Affiliation:
Girton CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The exact solution for a trapezoidal potential barrier is given in terms of Airy functions and trigonometrical functions. Numerical values are found for the ratio of the amplitudes of the transmitted and reflected waves. These are compared with those given by the WKBJ approximation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 2 , April 1956 , pp. 273 - 279
Copyright
Copyright © Cambridge Philosophical Society 1956

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Gamow, G. and Critchfield, C. L.Theory of atomic nucleus and nuclear energy-sources (Oxford, 1949), p. 160.Google Scholar
(2)Jeffreys, B.Proc. Camb. phil. Soc. 38 (1942), 401–5.CrossRefGoogle Scholar
(3)Jeffreys, H.Proc. Camb. phil. Soc. 52 (1956), 61–6.Google Scholar
(4)Langer, R. E.Bull. Amer. math. Soc. 40 (1934), 545–82.CrossRefGoogle Scholar
(5)Miller, J. C. P.British Association mathematical tables, part-vol. B. The Airy integral (London, 1946), pp. 1–56.Google Scholar
(6)Mott, N. F. and Sneddon, I. N.Wave mechanics and its applications (Oxford, 1948), p. 22.Google Scholar