Abstract
The gap between asymptotically degenerate eigenvalues of one-dimensional Schrödinger operators is estimated. The procedure is illustrated for two examples, one where the solutions of Schrödinger's equation are explicitly known and one where they are not. For the latter case a comparison theorem for ordinary differential equations is required. An incidental result is that a semiclassical (W-K-B) method gives a much better approximation to the logarithmic derivative of a wave-function than to the wave-function itself; explicit error-bounds for the logarithmic derivative are given.
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Communicated by A. Jaffe
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Harrell, E.M. On the rate of asymptotic eigenvalue degeneracy. Commun.Math. Phys. 60, 73–95 (1978). https://doi.org/10.1007/BF01609474
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DOI: https://doi.org/10.1007/BF01609474