  Physical states of the superstring can be described in light-cone gauge by
acting with transverse bosonic $\alpha_{-n}^{j}$ and fermionic
$\bar{q}_{-n}^{\dot{a}}$ operators on an $SO\left(8\right)$-covariant
superfield where $j,\dot{a}=1$ to $8$. In the pure spinor formalism, these
states are described in an $SO\left(9,1\right)$-covariant manner by the
cohomology of the BRST charge $Q=\frac{1}{2\pi
i}\oint\lambda^{\alpha}d_{\alpha}$. In this paper, a similarity transformation
is found which simplifies the form of $Q$ and maps the light-cone description
of the superstring vertices into DDF-like operators in the cohomology of $Q$.
