  Following Schnabl's analytic solution to string field theory, we calculate
the operators ${\cal L}_0,{\cal L}_0^\dagger$ for a scalar field in the
continuous $\kappa$ basis. We find an explicit and simple expression for them
that further simplifies for their sum, which is block diagonal in this basis.
We generalize this result for the bosonized ghost sector, verify their
commutation relation and relate our expressions to wedge state representations.
