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On the unit tangent bundle of a compact Riemannian surface of constantnonzero curvature, we study semiclassical Schr{\"o}dinger operators associatedwith the natural sub-Riemannian Laplacian built along the horizontal bundle. Inthat setup , the involved Reeb flow is periodic and we show that high-frequencySchr{\"o}dinger eigenfunctions enjoy extra regularity properties. As anapplication, we derive regularity properties for low-energy eigenmodes ofsemiclassical magnetic Schr{\"o}dinger operators on the underlying surface byconsidering joint eigenfunctions with the Reeb vector field.

Asymptotic regularity of sub-Riemannian eigenfunctions in dimension 3: the periodic case