| Résume | Résumé : In this talk, we address the problem of defining the Schrödinger evolution on surfaces embedded in $3$-dimensional contact sub-Riemannian manifolds. Specifically, after introducing a geometrically natural Schrödinger operator on a surface $S$, we investigate whether it is essentially self-adjoint. We show that its essential self-adjointness is related to the geometry of $S$, and in particular to invariants associated with its singular (characteristic) points. Finally, we analyze self-adjoint extensions through an explicit example: on the one hand, we define extensions that yield disjoint dynamics, and on the other hand, we introduce "Kirchhoff-type" extensions, which allow interactions between different leaves. |
