Twisted de Rham differential ($d_h=e^{-h}d{e}^h$)

For a real function $h$, the twisted de Rham differential is $d_h=d+dh\wedge =e^{-h}d{e}^h$. Its adjoint and $d_h$ define a supersymmetric Hamiltonian, and its square-integrable cohomology describes zero-energy states.