L 2-exponential lower bounds to solutions of the Schr�dinger equation
Copyright policy )L 2-exponential lower bounds to solutions of the Schr�dinger equation
We study decay properties of solutions ϕ of the Schrodinger equation (−Δ+V)ϕ=Eϕ. Typical of our results is one which shows that ifV=o(|x|−1/2) at infinity or ifV is a homogeneousN-body potential (for example atomic or molecular), then ifE \sqrt { - E} ,e^{\alpha \left| x \right|} \psi \notin L^2 \left( {\mathbb{R}^n } \right)$$ . We also construct examples to show that previous essential spectrum-dependent upper bounds can be far from optimal if ϕ is not the ground state.
- University of Vienna Austria
- Mittag-Leffler Institute Sweden
- Royal Swedish Academy of Sciences Sweden
81F05, Schrödinger operator, Schrödinger equation, N-body potential, 35J10, 47F05, exponential lower bounds, 81C05, Stability in context of PDEs
81F05, Schrödinger operator, Schrödinger equation, N-body potential, 35J10, 47F05, exponential lower bounds, 81C05, Stability in context of PDEs
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