Density of quasilocalized states along the resonance curves in continuum

Densities of quasilocalized states are calculated and analyzed for a one-dimensional system with a point defect and an FCC crystal with a planar defect. The density of states displays a pronounced peak that is positioned near the energy (frequency) of resonant transmission of a particle (wave) through the defect but slightly shifted from this energy. The peak nears the resonance frequency and sharpens, tending to a $\delta$ function, as the continuum edge is approached.