  We study the dynamical correlations of nonintegrable systems with quantum
many-body scar (QMBS) states generated by a ladder operator. The spectral
function of the ladder operator has an exact $\delta$-function peak induced by
the QMBS states. As a concrete example, we show that in the one-dimensional
(1D) spin-$1$ Affleck-Kennedy-Lieb-Tasaki model, the spectral function of
two-magnon excitations exhibits a characteristic bow-tie shape composed of a
$\delta$-function resonance peak at momentum $k=\pi$ and a continuum spectrum
elsewhere. The two-magnon excitations can be observed with the resonant
inelastic X-ray scattering spectroscopy on quasi-1D nickelates and other
spin-$1$ antiferromagnetic materials, thus it paves the way to detecting the
(approximate) QMBS states in realistic materials.
