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We study the wave equation on the real line with a potential that falls offlike $|x|^{-\alpha}$ for $|x| \to \infty$ where $2 < \alpha \leq 4$. We provethat the solution decays pointwise like $t^{-\alpha}$ as $t \to \infty$provided that there are no resonances at zero energy and no bound states. As anapplication we consider the $\ell=0$ Price Law for Schwarzschild black holes.This paper is part of our investigations into decay of linear waves on aSchwarzschild background.

Decay estimates for the one-dimensional wave equation with an inverse power potential