  We have analytically explored the quantum phenomenon of particle scattering
by harmonically trapped Bose and Fermi gases with the short ranged (Fermi-Huang
$\delta^3_p$ [1]) 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) 3-D harmonically trapped interacting Bose-Einstein
condensate (BEC), (ii) BECs in a double well, and (iii) BECs in an optical
lattice.
