  Energies and wave functions are calculated for d-wave quasiparticles in the
mixed state using the formalism of Franz and Tesanovic for the low-lying energy
levels. The accuracy of the plane-wave expansion is explored by comparing
approximate to exact results for a simplified one-dimensional problem, and the
convergence of the plane- wave expansion to the two-dimensional case is
studied. The results are used to calculate the low-energy tunneling density of
states and the low-temperature specific heat, and these theoretical results are
compared to semiclassical treatments and to the available data. Implications
for the muon spin resonance measurements of vortex core size are also
discussed.
