Perturbations of Non Self-adjoint Sturm-liouville Problems, with Applications to Harmonic Oscillators
نویسنده
چکیده
We study the behavior of the limit of the spectrum of a non self-adjoint Sturm-Liouville operator with analytic potential as the semiclassical parameter h → 0. We get a good description of the spectrum and limit spectrum near ∞. We also study the action of one special perturbation of the operator (adding a Heaviside function), and prove that the limit spectrum is very unstable. As an illustration we describe the limit spectrum as h → 0 for P h = −h∆+ ix and the effect of this perturbation.
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