Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-13T07:44:22.404Z Has data issue: false hasContentIssue false
  • English
  • Français

XXV.—Some Continuant Determinants arising in Physics and Chemistry

Published online by Cambridge University Press:  14 February 2012

D. E. Rutherford
D. E. Rutherford
Affiliation:
United College, University of St Andrews
Get access Rights & Permissions [Opens in a new window]

Extract

In many problems in physics and chemistry certain determinants of large order and of a special type require to be evaluated. The determinants in question usually arise from some kind of secular equation, and in most cases they owe their origin to a system of particles of one kind or another which, in their equilibrium positions, form a regular lattice, each particle being acted upon by its nearest neighbours and perhaps by a fixed boundary. These forces may be assumed to be elastic in character, to the degree of approximation required. For simplicity we shall refer to these particles as atoms although they may be electrons, molecules or even material particles in the Newtonian sense, according to the nature of the problem under investigation. In particular we may mention the occurrence of these determinants in problems involving the solution of Schrödinger's Wave Equation for permitted energy levels and in determining the distribution of electric charge in crystals, metals and large molecules. They have also been used by Born in his investigations of crystal structure by means of X-rays. It is hoped therefore that the results achieved in this paper will be of interest to the physicist and chemist as well as to the mathematician.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 62 , Issue 3 , 1948 , pp. 229 - 236
Copyright
Copyright © Royal Society of Edinburgh 1946

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 TO LITERATURE

Born, M., 1942. “Lattice dynamics and X-ray scattering”, Proc. Phys. Soc., LIV, 362.Google Scholar
Coulson, C. A., 1938. “The electronic structure of some polyenes and aromatic molecules IV”, Proc. Roy. Soc, A, CLXIV, 383.Google Scholar
Goodwin, E. T., 1939. “Electronic states at the surfaces of crystals”, Proc. Camb. Phil. Soc., XXXV, 221.CrossRefGoogle Scholar
Ledermann, W., 1944. “Asymptotic formulae relating to the physical theory of crystals”, Proc Roy. Soc, A, CLXXXli, 362.Google Scholar
Lennard-Jones, J. E., 1937. “The electronic structure of some polyenes and aromatic molecules I”, Proc Roy. Soc., A, CLVIII, 208.Google Scholar
Lennard-Jones, J. E., and Turkevich, J., 1937. “The electronic structure of some polyenes and aromatic molecules II”, Proc. Roy. Soc., A, CLVIII, 297.Google Scholar
MacDuffee, C. C, 1933. The Theory of Matrices, Berlin.CrossRefGoogle Scholar
Muir, T., 1923. History of the Theory of Determinants IV, London.Google Scholar