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We have calculated the zero-temperature binding energy of a single impurityatom immersed in a Bose-Einstein condensate of ultracold atoms that are trappedin an axially symmetric harmonic potential, where the impurity interacts withbosonic atoms in the condensate via a low-energy s-wave scattering. In thiscase, bosons are excited around the impurity to form a quasiparticle, namely, aBEC polaron. We have developed a variational method, {\it a la} Lee-Low-Pines(LLP) theory for electron-phonon systems, for description of the polaron with aconserved angular momentum around the symmetric axis. It is found in numericalresults that the binding energy between the impurity and the excited bosonsbreak the degeneracy with respect to the total angular momentum of the polaron.The angular momentum is partially shared by the excited bosons, which is due toa mechanism similar to the drag effect on the polaron momentum by a phononcloud in the LLP theory.

BEC polaron in harmonic trap potential at weak coupling regime: Lee-Low-Pines type approach