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We study the wave equation on the real line with a potential that falls off like | x | − α   forwhere 2 &lt;  α  ≤ 4. We prove that the solution decays pointwise like  t  − α   asprovided that there are no resonances at zero energy and no bound states. As an application, we consider thePrice Law for Schwarzschild black holes. This paper is part of our investigations into decay of linear waves on a Schwarzschild background, see [ 5 ,  6 ].

Decay Estimates for the One-dimensional Wave Equation with an Inverse Power Potential