2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57816We study the Complex Absorbing Potential (CAP) Method in computing quantum resonances of width $c(h) = O(h^N)$, $N\gg1$. We show that up to $h^{-M}\sqrt{c(h)} +\Oh$ error, $M\gg1$, resonances are perturbed eigenvalues of the CAP Hamiltonian $P(h)-iW$, and vice versa, where $W$ is the CAP with non-negative real part supported outside the trapping region. In some cases, the error terms are exponentially small.Mathematical PhysicsAnalysis of PDEs35P25, 35P20, 47A40, 81Q20text