Bargmann's limit

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

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)


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