Related papers: Schr\"{o}dinger operators with distributional pote…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
We prove a bound, of Bargmann- Birman-Schwinger type, on the number of eigenvalues of the matrix Schr\"odinger operator on the half line, with the most general self adjoint boundary condition at the origin, and with selfadjoint matrix…
We discuss properties of $L^2$-eigenfunctions of Schr\"odinger operators and elliptic partial differential operators. The focus is set on unique continuation principles and equidistribution properties. We review recent results and announce…
The discrete one-dimensional Schr\"odinger operator is studied in the finite interval of length $N=2 M$ with the Dirichlet boundary conditions and an arbitrary potential even with respect to the spacial reflections. It is shown, that the…
Estimates for eigenvalues of Schr\"{o}dinger operators on the half-line with complex-valued potentials are established. Schr\"{o}dinger operators with potentials belonging to weak Lebesque's classes are also considered. The results cover…
In this work, we consider not only a discontinuous boundary-value problem with retarded argument and four supplementary transmission conditions at the two points of discontinuities but also, eigenparameter-dependent boundary conditions and…
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…
This work deals with an inverse problem for the Sturm-Liouville operator with non-separated boundary conditions, one of which linearly depends on a spectral parameter. Uniqueness theorem is proved, solution algorithm is constructed and…
The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…
The inverse scattering problem for the Schr$\mathrm{\ddot{o}}$dinger operators on the line is considered when the potential is real valued and integrable and has a finite first moment. It is shown that the potential on the line is uniquely…
We characterize the location and number of eigenvalues for the Lax operator associated to the one-dimensional cubic nonlinear defocusing Schr\"odinger equation. With the help of a newly discovered unitary matrix, the analysis reduces to the…
We analyse the exact solutions of a conditionally-solvable Schr\"odinger equation with a rational potential. From the nodes of the exact eigenfunctions we derive a connection between the otherwise isolated exact eigenvalues and the actual…
Schr\"{o}dinger operators of the form $\Delta - W$ on $L^2_{\text{rad}}(\mathbb{R}^3)$, the space of radially symmetric square integrable functions are relevant in a variety of physical contexts. The potential $W$ is taken to be radially…
This note points out some bounds for the number of negative eigenvalues of Schroedinger operators with Hardy-type potentials, which follow from a simple coordinate transformation, and could prove useful in a spectral analysis of certain…
A third order self-adjoint differential operator with periodic boundary conditions and an one-dimensional perturbation has been considered. For this operator, we first show that the spectrum consists of simple eigenvalues and finitely many…
The principal purpose of this note is to provide a reconstruction procedure for distributional matrix-valued potential coefficients of Schr\"odinger-type operators on a half-line from the underlying Weyl-Titchmarsh function.
We consider the Schr\"{o}dinger operator on a finite interval with an $L^1$-potential. We prove that the potential can be uniquely recovered from one spectrum and subsets of another spectrum and point masses of the spectral measure (or…
The matrix Sturm-Liouville operator on a finite interval with the boundary conditions in the general self-adjoint form and with the singular potential from the class $W_2^{-1}$ is studied. This operator generalizes Sturm-Liouville operators…
We work with the Friedrichs extension of a one dimensional Schrodinger whose potential has a certain type of regular singularity near one end point. We study the effect on the eigenvalues of shrinking the region slightly near the end point.…
We give an explicit correspondence between the domains of the self-adjoint extensions of a one-dimensional Schr\"odinger differential operator with symmetric real-valued potential and the boundary conditions the functions in the resulting…