Approximating resonances with the Complex Absorbing Potential Method

Details Approximating resonances with the Complex Absorbing Potential Method Approximating resonances with the Complex Absorbing Potential Method

2004-09-09

arxiv.org/abs/math-ph/0409020v1

Physics

Mathematical Physics

Scientific paper

We 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.

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