Some inverse spectral results for semi-classical Schrödinger operators

V. Guillemin; A. Uribe

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Some inverse spectral results for semi-classical Schrödinger operators

V. Guillemin·A. Uribe

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Abstract

We consider a semi-classical Schrödinger operator, -h^2Δ+ V(x). Assuming that the potential admits a unique global minimum and that the eigenvalues of the Hessian are linearly independent over the rationals, we show that the low-lying eigenvalues of the operator determine the Taylor series of the potential at the minimum.

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V. Guillemin, A. Uribe. 2005-09-13. Some inverse spectral results for semi-classical Schrödinger operators. https://arxiv.org/abs/math/0509290

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