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In this Letter the problem of the existence of a state localized on a weakshort-range attractive potential in the presence of dissipation is considered.It is shown that, contrary to the pure quantum case, a localized state isproduced in any number of dimensions, while in low dimensions dissipation leadsto much stronger localization. The results have physical implications for thedissipative dynamics of objects such as heavy particles in Fermi liquids andfor superconductivity in high-$T_c$ materials.Comment: RevTeX, 4 pages, 1 figure. Published versio

Localization on Short-Range Potentials in Dissipative Quantum Mechanics