Schrödinger operators with distributional potentials and boundary conditions dependent on the eigenvalue parameter

Abstract

We study various direct and inverse spectral problems for the one-dimensional Schrödinger equation with distributional potential and boundary conditions containing the eigenvalue parameter.

28 pages, very minor corrections, published version. arXiv admin note: text overlap with arXiv:1708.07497

References in corpus (7)

• Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials
• Inverse spectral problems for Sturm-Liouville operators with singular potentials
• Half-inverse spectral problems for Sturm--Liouville operators with singular potentials
• Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions
• Essentially isospectral transformations and their applications
• Regularization of singular Sturm-Liouville equations
• Inverse spectral problems for Sturm-Liouville operators with singular potentials, II. Reconstruction by two spectra

Cited by in corpus (10)

• Linear differential operators with distribution coefficients of various singularity orders
• Inverse square singularities and eigenparameter dependent boundary conditions are two sides of the same coin
• Reconstruction of higher-order differential operators by their spectral data
• A Riesz basis criterion for Schrödinger operators with boundary conditions dependent on the eigenvalue parameter
• The number of Dirac-weighted eigenvalues of Sturm-Liouville equations with integrable potentials and an application to inverse problems
• Spectral identities for Schrödinger operators
• Uniform stability for the inverse Sturm-Liouville problem with eigenparameter-dependent boundary conditions
• Contact interactions, self-adjoint extensions, and low-energy scattering
• A non-degeneracy theorem for interacting fermions in one dimension
• Regularization of energy-dependent pointlike interactions in 1D quantum mechanics