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

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

2004-01-12

arxiv.org/abs/math-ph/0401023v1

J. Phys. A36, 9907 (2003)

Physics

Mathematical Physics

7 pages

Scientific paper

10.1088/0305-4470/36/38/308

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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