Degenerate Schrödinger equations with irregular potentials

In this work, we investigate a class of degenerate Schrödinger equations associated to degenerate elliptic operators with irregular potentials on [Formula: see text] by introducing a suitable Hörmander metric [Formula: see text] and a [Formula: see text]-weight [Formula: see text]. We establish the well-posedness for the corresponding degenerate Schrödinger and degenerate parabolic equations. When the subellipticity is available on the degenerate elliptic operator we deduce spectral properties for a class of degenerate Hamiltonians. We also investigate the [Formula: see text] mapping properties for operators with symbols in the [Formula: see text] classes in the spirit of classical Fefferman’s [Formula: see text]-bounds for the [Formula: see text] calculus. Finally, within our [Formula: see text]-classes, sharp [Formula: see text]-estimates and Schatten–von Neumann properties for Schrödinger operators for Hörmander sums of squares are also investigated.