Talk by Joachim Kerner

In this talk we discuss recent results on the spectral gap of one-dimensional Schrödinger operators in the limit of large intervals. The spectral gap, being defined as the difference between the first two eigenvalues, is a classical object in the spectral theory of \linebreak operators but it also appears frequently in more applied settings. As a main objective, we will derive upper and lower bounds on the spectral gap for certain (and quite general) classes of potentials. Doing this, we will also come across some relatively surprising findings (partially, this is based on joint work with M. Täufer (Hagen)).