Some structural properties of the energy eigenfunctions of an electron in a finite-dipole field are analyzed, in particular the asymptotic behavior when the electron is far away, and the coalescence and cusp properties when it is close to the dipole charges. Model wave functions incorporating these properties are developed, which give accurate values for the energies and some other quantities, and a useful insight into the physical structure of the system. Critical radius for the existence of the bound states is obtained from the Wentzel-Kramers-Brillouin approach. These considerations are extended to the description of the system in two dimensions.(C) 2004 American Institute of Physics.