Explicit formula for Schroedinger wave operators on the half-line for potentials up to optimal decay

11 Mar 2019  ·  Inoue Hideki ·

We give an explicit formula for the wave operators for Schroedinger operators on the half-line with a potential decaying strictly faster than the polynomial of degree minus two. The formula consists of the main term given by the scattering operator and a function of the generator of the dilation group, and a Hilbert-Schmidt remainder term... Our method is based on the elementary construction of the generalized Fourier transform in terms of the solutions of the Volterra integral equations. As a corollary, a topological interpretation of Levinson's theorem is established via an index theorem approach. read more

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Functional Analysis Mathematical Physics Mathematical Physics