Some inverse spectral results for semi-classical Schrödinger operators

Details Some inverse spectral results for semi-classical Schrödinger operators Some inverse spectral results for semi-classical Schrödinger operators

2005-09-13

arxiv.org/abs/math/0509290v1

Mathematics

Spectral Theory

13 pages

Scientific paper

We consider a semi-classical Schr\"odinger operator, -h^2\Delta + 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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