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Renormalization group equations for the physical t matrix are written for quantum scattering with some potentials singular at the origin in two and three dimensions. The momentum-space perturbative treatment of these scattering problems exhibits ultraviolet divergences and permits renormalization leading to a scale. These equations yield the correct asymptotic behavior and some low-energy properties of the t matrix. Illustrations are made for the Dirac delta potential in two and three dimensions.doi:10.1103/physrevlett.74.4572 pmid:10058544 fatcat:ubqlocjqurbi3k6y6gemb2sfnq