  The operator formalism of the first quantized string theory is applied to the
stringy excitations in the linear dilaton background. In particular, the
normal-ordered vertex operators in the old-covariant spectrum of the bosonic
open string, which correspond to the physical state solutions of the Virasoro
constraints, are shown to satisfy the conformal algebra. Tree-level scattering
amplitudes among different stringy states are computed using the coherent-state
method and the modified inner product of the Hilbert space. Decoupling of the
zero-norm states, i.e., the on-shell stringy Ward identities are shown to hold
for all tree-level amplitudes under consideration.
