  Employing the spin-wave formalism within and beyond the harmonic-oscillator
approximation, we study the dynamic structure factors of spin-$\frac{1}{2}$
nearest-neighbor quantum Heisenberg antiferromagnets on two-dimensional
quasiperiodic lattices with particular emphasis on a magnetic analog to the
well-known confined states of a hopping Hamiltonian for independent electrons
on a two-dimensional Penrose lattice. We present comprehensive calculations on
the $\mathbf{C}_{5\mathrm{v}}$ Penrose tiling in comparison with the
$\mathbf{C}_{8\mathrm{v}}$ Ammann-Beenker tiling, revealing their decagonal and
octagonal antiferromagnetic microstructures. Their dynamic spin structure
factors both exhibit linear soft modes emergent at magnetic Bragg wavevectors
and have nearly or fairly flat scattering bands, signifying magnetic
excitations localized in some way, at several different energies in a
self-similar manner. In particular, the lowest-lying highly flat mode is
distinctive of the Penrose lattice, which is mediated by its unique
antiferromagnons confined within tricoordinated sites only, unlike their
itinerant electron counterparts involving pentacoordinated as well as
tricoordinated sites. Bringing harmonic antiferromagnons into higher-order
quantum interaction splits the lowest-lying nearly flat scattering band in two,
each mediated by further confined antiferromagnons, which is fully demonstrated
and throughly visualized in the perpendicular as well as real spaces. We
disclose superconfined antiferromagnons on the two-dimensional Penrose lattice.
