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Diverging eigenvalues in domain truncations of Schrödinger operators with complex potentials are analyzed and their asymptotic formulas are obtained. Our approach also yields asymptotic formulas for diverging eigenvalues in the strong coupling regime for the imaginary part of the potential. [ABSTRACT FROM AUTHOR]

We study spectral approximations of Schrödinger operatorsT = −Δ+Qwith complex potentials on Ω = ℝd, or exterior domains Ω⊂ℝd, by domain truncation. Our weak assumptions cover wide classes of potentialsQfor whichThas discrete spectrum, of approximating domains Ωn, and of boundary conditions on∂Ωnsuch as mixed Dirichlet/Robin type. In particular,Re Qneed not be bounded from below andQmay be singular. We prove generalized norm resolvent convergence and spectral exactness,i.e.approximation ofalleigenvalues ofTby those of the truncated operatorsTnwithoutspectral pollution. Moreover, we estimate the eigenvalue convergence rate and prove convergence of pseudospectra. Numerical computations for several examples, such as complex harmonic and cubic oscillators ford = 1,2,3, illustrate our results. [ABSTRACT FROM AUTHOR]