Inverse Problem for the Schr\"odinger Operator in an Unbounded Strip

We consider the operator $H:= i \partial_t + \nabla \cdot (c \nabla)$ in an unbounded strip $\Omega$ in $\mathbb{R}^2$, where $c(x,y) \in \mathcal{C}^3(\bar{\Omega})$. We prove adapted a global Carleman estimate and an energy estimate for this operator. Using these estimates, we give a stability result for the diffusion coefficient $c(x,y)$.