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We present a new theoretical framework for describing an impurity in atrapped Bose system in one spatial dimension. The theory handles any externalconfinement, arbitrary mass ratios, and a weak interaction may be includedbetween the Bose particles. To demonstrate our technique, we calculate theground state energy and properties of a sample system with eight bosons andfind an excellent agreement with numerically exact results. Our theory can thusprovide definite predictions for experiments in cold atomic gases.

Quantum Impurity in a One-dimensional Trapped Bose Gas