Water potential: Difference between revisions

Revision as of 05:34, 29 January 2014

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} \leq \frac{1}{2 l + 1} \frac{2 m}{ℏ^{2}} \int_{0}^{\infty} r | V (r) |_{V < 0} d r

Note that the Dirac delta function potential attains this limit.

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+{{Orphan|date=February 2009}}
+In [[quantum mechanics]], '''Bargmann's limit''', named for [[Valentine Bargmann]], provides an [[upper bound]] on the number ''N''<sub>''l''</sub> of [[bound state]]s in a system. It takes the form
+:<math>N_l \leq \frac{1}{2l+1} \frac{2m}{\hbar^2} \int_0^\infty r |V(r)|_{V<0}\, dr</math>
+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)
+{{quantum-stub}}
+[[Category:Quantum mechanics]]