[en] We have analytically explored the quantum phenomenon of particle scattering by harmonically trapped Bose gases with the short ranged Fermi-Huang delta interactions among the incident particle and the scatterers. We have predicted differential scattering cross-sections and their temperature dependence in this regard. Coherent scattering even by a single boson or fermion in the finite geometry gives rise to new tool of determining energy eigenstate of the scatterer. Our predictions on the differential scattering cross-sections can be tested within the present day experimental setups, specially for (i) 3D harmonically trapped interacting Bose-Einstein condensate (BEC), (ii) BECs in a double well, and (iii) BECs in an optical lattice. (author)