Lieb-Thirring inequality with semiclassical constant and gradient error term (Q1694694)

This short article presents an improved lower bound on the kinetic energy for fermions. Lieb and Thirring are credited for establishing a semiclassical lower bound which agrees with the Thomas-Fermi approximation up to a constant factor. Here, the author provides a lower bound with the semiclassical constant and a lower order gradient error term. The main result implies the Lieb-Thirring inequality (without a sharp constant).