XI.On the variation calculation of eigen values

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Abstract
The variation calculation of the eigen values associated with a differential system provides an upper bound for the least eigen value. There is no indication of the error involved in the approximation. An estimate of the accuracy of the approximation may be obtained if a lower bound for the eigen value is also known. An expression for such a lower bound is established and compared with an alternative expression due to D. H. Weinstein. Illustrative calculations are given for two simple problems in wave mechanics. The bound set up in this paper is analogous to, but of wider application than, a result obtained by E. Trefftz for the eigen values associated with integral equations.

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