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Spectral asymptotics for perturbed spherical Schrödinger operators and applications to quantum scattering. (English) Zbl 1284.34130
The authors investigate perturbed spherical Schrödinger operators with a real-valued potential in an arbitrary space dimension. They first establish the high energy asymptotics of the singular Weyl function and the associated spectral measure for those operators. Their innovative approach uses a one-term asymptotic formula for the \(m\)-function, along with the commutation method for Bessel operators.
A Liouville type transform is used in the proof. The authors then enumerate examples of the usefulness of their findings including, among them the application to the quantum mechanical scattering problem. Results on the asymptotic behavior of \(m\)-functions of regular Sturm-Liouville problems are listed in the appendix.

MSC:
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34L05 General spectral theory of ordinary differential operators
34B20 Weyl theory and its generalizations for ordinary differential equations
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