Resonance matching of 2-$\delta$ and 3-$\delta$ potentials in 1D Quantum Scattering

We investigate whether a 3-$\delta$ system with positive coupling strengths can approximate the transmission spectrum of a 2-$\delta$ resonance system with opposite-sign couplings for $k<3$. Theoretical analysis establishes exact isospectrality – perfectly matched transmission spectrum – is impossible for physically non-trivial configurations, while numerical experiments identify the minimal constraint set for practicability. These results establish both the practical limits and achievable accuracy of resonance matching under sign constraints, with implications for understanding spectral non-uniqueness in quantum scattering problems.