Bargmann's limit

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

$N_l \leq \frac{1}{2l+1} \frac{2m}{\hbar^2} \int_0^\infty r |V(r)|_{V<0}\, dr$

Note that the Dirac delta function potential attains this limit.

References

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