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Necessary and sufficient conditions for existence of bound states in a central potential

Fabian Brau
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Abstract

We obtain, using the Birman-Schwinger method, a series of necessary conditions for the existence of at least one bound state applicable to arbitrary central potentials in the context of nonrelativistic quantum mechanics. These conditions yield a monotonic series of lower limits on the "critical" value of the strength of the potential (for which a first bound state appears) which converges to the exact critical strength. We also obtain a sufficient condition for the existence of bound states in a central monotonic potential which yield an upper limit on the critical strength of the potential.

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Fabian Brau. 2004-01-12. Necessary and sufficient conditions for existence of bound states in a central potential. https://doi.org/10.1088/0305-4470/36/38/308

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