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We present a detailed comparison of numerical solutions of the quasiclassicalEilenberger equations with several approximation schemes for the density ofstates of s- and d-wave superconductors in the vortex state, which have beenused recently. In particular, we critically examine the use of the Dopplershift method, which has been claimed to give good results for d-wavesuperconductors. Studying the single vortex case we show that there areimportant contributions coming from core states, which extend far from thevortex cores into the nodal directions and are not present in the Doppler shiftmethod, but significantly affect the density of states at low energies. Thisleads to sizeable corrections to Volovik's law, which we expect to be sensitiveto impurity scattering. For a vortex lattice we also show comparisons with themethod due to Brandt, Pesch, and Tewordt and an approximate analytical method,generalizing a method due to Pesch. These are high field approximationsstrictly valid close to the upper critical field Bc2. At low energies theapproximate analytical method turns out to give impressively good results overa broad field range and we recommend the use of this method for studies of thevortex state at not too low magnetic fields.Comment: 11 pages, 11 figures; revised version, error in Fig. 6b remove

Spectrum of low-energy excitations in the vortex state: Comparison of the Doppler-shift method to a quasiclassical approach