Hundertmark D., Lieb E.H., Thomas L.E.
A Sharp Bound for an Eigenvalue Moment of the One-Dimensional  
    Schr\"{o}dinger Operator
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ABSTRACT.  We give a proof of the Lieb-Thirring inequality in the critical 
case $d=1$, $\gamma= 1/2$, which yields the best possible constant.