This limit is the best possible upper bound in such a way that for a given ℓ ℓ , one can always construct a potential V ℓ ℓ for which N ℓ ℓ is arbitrarily close to this upper bound. Note that the Dirac delta function potential attains this limit. After the first proof of this inequality by Valentine Bargmann in 1953, Julian Schwinger presented an alternative way of deriving it in 1961.