A Lieb-Thirring inequality bounds a sum of powers of the negative eigenvalues of a Schrödinger operator by an integral of its potential (Lieb and Thirring 1976). In
one dimension, write 
on 
with 
. For 
, the inequality
has the form
 |
where the negative eigenvalues are counted with multiplicity. The optimal constant is the least 
that works for every admissible potential. The semiclassical
value is
 |
where 
is the gamma function.
