On the Schrödinger Operators with Eigenvalues Embedded into Absolutely Continuous Spectrum
Year: 2026
Type: article
Abstract: In this paper, we consider the Schrödinger operator on \(L^2(0,\infty )\) given by \((Hu)(x)=-u''(x)+V(x)u(x)\) with a self-adjoint boundary condition at 0, where V ( x ) is the real perturbation. It is well known that under \(L^2(0,\infty )\) perturbations the absolutely continuous spectrum of H on the positive semi-axis is preserved. In this paper, by the technique of modified Prüfer transformation and constructive methods, we prove that, with a class of smooth perturbations, H has exactly the given eigenvalues embedded into the absolutely continuous spectrum.
Authors: Kang Lyu, Chuanfu Yang
Institution: Nanjing University of Science and Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $1,490
OpenAlex ID: W7148834947