  We investigate how the presence of a localized impurity in a Bose-Einstein
condensate of trapped cold atoms that interact with each other weakly and
repulsively affects the profile of the condensed and excited components at zero
temperature. By solving the Gross-Pitaevskii and Bogoliubov-de Gennes
equations, we find that an impurity-boson contact attraction (repulsion) causes
both components to change in spatial structure in such a way as to be enhanced
(suppressed) around the impurity, while slightly declining (growing) in a far
region from the impurity. Such behavior of the quantum depletion of the
condensate can be understood by decomposing the impurity-induced change in the
profile of the excited component with respect to the radial and azimuthal
quantum number. A significant role of the centrifugal potential and the "hole"
excitation level is thus clarified.
