In quantum mechanics, Bargmann's limit provides an upper bound on the number N_l of bound states in a system. It takes the form

Professor Hagen says, "The Bargmann limit provides, if not the best bound, a pretty darn good one."

Note that the delta function potential attains this limit.

References

• Bargmann, Proc. Nat. Acad. Sci. 38 961 (1952)
• Schwinger, Proc. Nat. Acad. Sci. 47 122 (1961)