We show that the complex absorbing potential method for computing scattering resonances applies to the case of exponentially decaying potentials. This means that the eigenvalues of −Δ + V − iɛx² and |V(x)| ≤ Ce^−2γ|x| converge, as ɛ → 0+, to the poles of the meromorphic continuation of ${(-\mathrm{\Delta }+V-{\lambda }^2)}^{-1}$ uniformly on compact subsets of Re λ > 0, Im λ > − γ, and arg λ > −π/8.

中文翻译：

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共振作为指数衰减电位的黏度极限

我们表明，用于计算散射共振的复杂吸收势方法适用于指数衰减势的情况。这意味着-Δ+的特征值V - iɛx ²和| V（x）| ≤策^{-2 γ | x |} 当ɛ →0+时，收敛到${（-\mathrm{\Delta }+\mathrm{伏特}-{\lambda }^{\mathrm{2个}}）}^{-\mathrm{1个}}$上均匀地重新的紧凑子组 λ > 0，林 λ > - γ，和Arg  λ > - π / 8。