The quantization of normal velocity does not concentrate on hypersurfaces.

We seek to extend work by Christianson–Hassell–Toth [3] on restrictions of Neumann data of Laplacian eigenfunctions to interior hypersurfaces to a general semiclassical setting. In the semiclassical regime the appropriate generalization is to study the restrictions of the functionv = ν(x,hD)uwhereν(x,hD) is the operator defined by quantizing the normal velocity observable. For the Laplacianwhereνis the normal to the hypersurface. We find thatprovideduis anquasimode of the semiclassical pseudodifferential operatorp(x,hD). This statement should be interpreted as a statement of non-concentration for the quantization of normal velocity. [ABSTRACT FROM AUTHOR]