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Boundary perturbations of some eigenvalue problems Julius, Robert Stanely

Abstract

In treating so-called "bounded quantum mechanical problems" one is generally led to difficult eigenvalue problems. For example, the problem of finding the wave equation for a hydrogen atom confined to a sphere of finite radius leads one to finding solutions of Laguerre's equation which vanish for given finite values of the independent variable. In this thesis we discuss three such problems in some detail. Since 1937 a number of papers on these problems have appeared; we describe here the principal methods of these papers, and improve one of them. We then develop a new method which is sufficiently general to treat each problem, and which can be established rigorously in each case. This method provides us with asymptotic expressions for the perturbed eigenvalues.

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