We will discuss Weyl laws with a sharp remainder term, in the 'integrated' (counting eigenvalues) and 'pointwise' (concerning the ground state density) forms. We will explain how the presence of a singular potential modifies the standard asymptotics. Since the microlocal approach of Levitan and Hörmander is not obvious to adapt in this setting, we will show how the older proof due to Avakumovic is well suited to include singular potentials. This is a joint work with Rupert Frank.
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