We prove a Lieb–Thirring inequality for Schrödinger operators [mathematical formula - see PDF] on the semi-axis with Robin boundary condition at the origin. The result improves on a bound obtained by P. Exner, A. Laptev, and M. Usman [Commun. Math. Phys. 362 (2014), 531–541] albeit under the additional assumption V ∈ L1(R+). The main difference in our proof is that we use the double commutation method in place of the single commutation method. We also establish an improved inequality in the case of a Dirichlet boundary condition.
Funding
VILLUM FONDEN through the QMATH Centre of Excellence (grant no. 10059)
VR grant 2017-04736 at the Royal Swedish Academy of Sciences
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