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We obtain, using the Birman-Schwinger method, a series of necessaryconditions for the existence of at least one bound state applicable toarbitrary central potentials in the context of nonrelativistic quantummechanics. These conditions yield a monotonic series of lower limits on the"critical" value of the strength of the potential (for which a first boundstate appears) which converges to the exact critical strength. We also obtain asufficient condition for the existence of bound states in a central monotonicpotential which yield an upper limit on the critical strength of the potential.Comment: 7 page

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