  Open string boundary conditions for non-BPS D-branes in type II string
theories discussed in hep-th/0505157 give rise to two sectors with integer (R
sector) and half-integer (NS sector) modes for the combined fermionic matter
and bosonic ghost variables in pure spinor formalism. Exploiting the manifest
supersymmetry of the formalism we explicitly construct the DDF (Del Giudice, Di
Vecchia, Fubini) states in both the sectors which are in one-to-one
correspondence with the states in light-cone Green-Schwarz formalism. We also
give a proof of validity of this construction. A similar construction in the
closed string sector enables us to define a physical Hilbert space in pure
spinor formalism which is used to project the covariant boundary states of both
the BPS and non-BPS instantonic D-branes. These projected boundary states take
exactly the same form as those found in light-cone Green-Schwarz formalism and
are suitable for computing the cylinder diagram with manifest open-closed
duality.
