  Quantized bound states at a vortex core are discretized in YNi$_2$B$_2$C. By
using scanning tunneling spectroscopy with an unprecedented 0.1 nm spatial
resolution, we find and identify the localized spectral structure, where in
addition to the first main peak with a positive low energy, a second subpeak
coming from the fourfold symmetric gap structure is seen inside the energy gap.
Those spectral features are understood by solving the Bogoliubov-de Gennes
equation for a fully three-dimensional gap structure. A particle-hole
asymmetric spectrum at the core site and quantum oscillation in the spectra are
clearly observed.
