The absence of positive energy bound states for a class of nonlocal potentials
Abstract
We generalize in this paper a theorem of Titchmarsh for the positivity of Fourier sine integrals. We then apply the theorem to derive simple conditions for the absence of positive energy bound states (bound states embedded in the continuum) for the radial Schrödinger equation with nonlocal potentials which are superpositions of a local potential and separable potentials.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- February 2005
- DOI:
- 10.1088/0305-4470/38/5/014
- arXiv:
- arXiv:math-ph/0409018
- Bibcode:
- 2005JPhA...38.1133C
- Keywords:
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- Mathematical Physics;
- Mathematics - Mathematical Physics
- E-Print:
- 23 pages