  We report self-consistent calculations of the microscopic electronic
structure of the so-called giant vortex states. These novel multiquantum vortex
states, detected by recent magnetization measurements on submicron disks, are
qualitatively different from the Abrikosov vortices in the bulk. We find that,
in addition to multiple branches of bound states in the core region, the local
tunneling density of states exhibits Tomasch oscillations due to the
single-particle interference arising from quantum confinement. These features
should be directly observable by scanning tunneling spectroscopy.
