  We investigate the scattering phenomena in two dimensions produced by a
general finite-range nonseparable potential. This situation can appear either
in a Cartesian geometry or in a heterostructure with cylindrical symmetry.
Increasing the dimensionality of the scattering problem new processes as the
scattering between conducting channels and the scattering from conducting to
evanescent channels are allowed. For certain values of the energy called
resonance energy the transmission through the scattering region changes
dramatically in comparison with an one-dimensional problem. If the potential
has an attractive character even the evanescent channels can be seen as dips of
the total transmission. The multi-channel current scattering matrix is
determined using its representation in terms of the R-matrix. The resonant
transmission peaks are characterized quantitatively through the poles of the
current scattering matrix. Detailed maps of the localization probability
density sustain the physical interpretation of the resonances. Our formalism is
applied to a quantum dot in a two-dimensional electron gas and to a conical
quantum dot dot embedded inside a cylindrical nanowire.
