  We report on a calculation of the quantized energy spectrum and quasiparticle
eigenfunctions for low lying excitations in the mixed state of clean d-wave
superconductors. Our study is based on an approximate analytical solution of
the Bogolubov-de Gennes equations for both rectangular and triangular flux
lattices with one of the primitive translations chosen parallel to the gap node
direction. For excitations with momenta close to a certain gap node we have
obtained a set of eigenfunctions which appear to be extended along the chosen
gap node direction and localized along the perpendicular one on a scale
determined by the intervortex distance. The periodic superfluid velocity field
induces a band structure in the spectrum, which depends essentially on the
vortex lattice geometry.
