  We investigate the properties of single-particle resonances in a
non-spherical potential by solving the coupled-channels equations for the
radial wave functions. We first generalize the box discretization method for
positive energy states to a deformed system. As in the spherical case, we find
that the discretized energy is stabilized against the box size when a resonance
condition is met. Using the wave functions thus obtained, we then discuss the
energy and the radial dependences of scattering wave functions in the vicinity
of an isolated resonance. In the eigenchannel basis, where the $S$-matrix is
diagonal, we propose a generalized expression for the factorization formula for
the multi-channel wave function. We find that the factorized wave function
agrees well with the exact solution inside the centrifugal barrier when the
energy distance from the resonance is less than the resonance width.
