In this paper, we are interested on the null controllability property of a linear degenerate Schrödinger equation with a degeneracy occurring on an interior subset of $$(0,1), \text{ that is, } \exists W_{1}\subset \subset (0,1), \text{ such that } \forall x\in W_{1}, \text{ } k(x)=0$$, where $$k$$ stands for the quantum diffusion. More precisely, we are concerned with the null controllability phenomenon using the classical procedure founded on a new Carleman estimate and afterward a newfangled observability inequality.