2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55238Energy-dependent Green's functions for the two and three dimensional $δ$-function plus harmonic oscillator potential systems are derived by incorporating the renormalization and the self-adjoint extension into the Green's function formalism, respectively. It is shown that both methods yield an identical Green's function if a certain relation between the self-adjoint extension parameter and the renormalized coupling constant is imposed.8 pages, RevtexHigh Energy Physics - Theorytext