We report the first self-consistent solution of the Bogolyubov-de Gennes eq
uation of a single vortex in pure d-wave superconductor. Contrary to popula
r belief, there are two groups of solutions: bound states and extended stat
es. For choosing p(F)xi = 1 similar to 2, where xi = nu(F)/Delta(0) is the
coherence length. wt: can describe at least qualitatively the quasi-particl
e spectrum around Vortices observed in YBCO and Bi2211. (C) 2000 Elsevier S
cience B.V. All rights reserved.