The Absence of Positive Energy Bound States for a Class of Nonlocal Potentials

Details The Absence of Positive Energy Bound States for a Class of Nonlocal Potentials The Absence of Positive Energy Bound States for a Class of Nonlocal Potentials

2004-09-08

arxiv.org/abs/math-ph/0409018v1

Physics

Mathematical Physics

23 pages

Scientific paper

10.1088/0305-4470/38/5/014

We generalize in this paper a theorem of Titchmarsh for the positivity of
Fourier sine integrals. We apply then the theorem to derive simple conditions
for the absence of positive energy bound states (bound states embedded in the
continuum) for the radial Schr\"odinger equation with nonlocal potentials which
are superposition of a local potential and separable potentials.

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