Mathematical Physics Seminar

In this talk I will approximate a Schrödinger operator on the real line by Jacobi operators to provide new proofs of sharp Lieb–Thirring inequalities. To this end I will first discuss spectral inequalities for Jacobi operators. Using the commutation method I will present a new proof of a sharp bound corresponding to a Lieb–Thirring inequality for the power 3/2. I will also introduce inequalities for higher powers of the eigenvalues as well as for matrix-valued potentials and compare the results to previously established bounds.