**Title:** L^{2}-restriction lower bounds for Schrodinger eigenfunctions in classically forbidden regions

**Speaker:** John Toth

**Speaker Info:** McGill University

**Brief Description:**

**Special Note**:

**Abstract:**

Let (M,g) be a compact, closed, real-analytic Riemannian manifold and P(h) = -h^{2}Δ_{g}+ V be a Schrodinger operator with (g,V) real-analytic. Given a regular energy value E with consider L^{2}-normalized eigenfunctions φ_{h}satisfying P(h) φ_{h}= ( E + o(1)) φ_{h}. We first prove that for any hypersurface H in the forbidden region Ω(E) = { V > E } there exists a constant c_{H}> 0 such that(a) ∫

We then use the estimate in (a) to prove that when dim M=2 and H is a C_{H}| φ_{h}|^{2}≥ e^{-cH/h}.^{ω}hypersurface in Ω(E), the nodal set Z_{ φh}= { φ_{h}= 0 } satifies the bound(b) # { Z

This is joint work with Yaiza Canzani._{ φh}∩ H } = O_{H}(h^{-1}).

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