A MATHEMATICAL TREATMENT OF THE PROBLEM OF DETERMINING THE EIGENVALUES ASSOCIATED WITH A PARTITION FUNCTION OF AN ATOM IN THE INTERIOR OF A PLASMA

摘要

This paper is concerned with the determination of the numerical values of some of the eigenvalues and the total number of eigenvalues of the differential equation x2p"+ [2dxe-x - k (k+1) - d2u2d2x2] P = O. The problem arises in treating the effective ioni¬zation potential of an atom in the interior of a plasma, but is essentially a mathematical problem.nThe problem is first treated from a theoretical standpoint. Then numerical tech¬niques are developed that lead to approximations of the eigenvalues'. An approximate inequality is obtained for the number of eigenvalues and an approximate equation is ob¬tained for the eigenvalues. Tabular data are shown listing a total of 55 of these eigen¬values for nine different cases.