The equation of motion a microparticle in various force fields is the Schr¨odinger wave equation.Many questions quantum mechanics, particular thermal radiation electromagneticwaves, lead to problem separability singular differential operators. One such operator isthe above Schr?dinger operator. In this paper, named studied by methods offunctional analysis. Found sufficient conditions for existe...

We present the extension of the successful Constant Perturbation Method (CPM) for Schrödinger problems to the more general class of Sturm-Liouville eigenvalue problems. Whereas the orginal CPM can only be applied to Sturm-Liouville problems after a Liouville transformation, the more general CPM presented here solves the Sturm-Liouville problem directly. This enlarges the range of applicability ...

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 illustrati...

Spectral inclusion and spectral pollution results are proved for sequences of linear operators the form T0 + i?sn on a Hilbert space, where sn is strongly convergent to identity operator ? > 0. We work in both an abstract setting more concrete Sturm–Liouville framework. The provide rigorous justification method computing eigenvalues gaps.