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The Complex Absorbing Potential (CAP) method is widely used to compute resonances in Quantum Chemistry, both for scalar valued and matrix valued Hamiltonians. In the semiclassical limit ℏ→0 we consider resonances near the real axis and we establish the CAP method rigorously in an abstract matrix valued setting by proving that resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa. The proof is based on pseudodifferential operator theory and microlocal analysis.
Kungsman, J. & Melgaard, M. (2010). Complex absorbing potential method for systems. Dissertationes Mathematicae, vol. 469, pg. 1-58. doi:10.4064/dm469-0-1