Water potential

Template:Orphan 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

$N_l\le \frac{1}{2l+1}\frac{2m}{{\hslash }^2}\underset{0}{\overset{\mathrm{\infty }}{\int }}r|V(r){|}_{V<0}dr$

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)