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In this paper, we consider the perturbations of the Harmonic OscillatorOperator by an odd pair of point interactions: $z (\delta(x - b) - \delta(x +b))$. We study the spectrum by analyzing a convenient formula for theeigenvalue. We conclude that if $z = ir$, $r$ real, as $r \to \infty$, thenumber of non-real eigenvalues tends to infinity.

Non-real eigenvalues of the Harmonic Oscillator perturbed by an odd, two-point $\delta$-potential