  In the presence of an external magnetic field, the low lying elementary
excitations of a d-wave superconductor have quantized energy and their momenta
are locked near the node direction. It is argued that these discrete states can
most likely be detected by a local probe, such as a scanning tunneling
microscope. The low temperature local tunneling conductance on the Wigner-Seitz
cell boundaries of the vortex lattice is predicted to show peaks spaced as $\pm
\sqrt{n}, n ={0,1,2, ...}$. The $n=0$ peak is anomalous, and it is present only
if the superconducting order parameter changes sign at certain points on the
Fermi surface. Away from the cell boundary, where the superfluid velocity is
nonzero, each peak splits, in general, into four peaks, corresponding to the
number of nodes in the order parameter.
