Some inverse spectral results for semi-classical Schr\"odinger operators
2005
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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