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In this letter new, closed and compact analytic expressions for the evaluation of resonant energies, resonant bound-states, eigenvalues and eigenfunctions for both scattering and bounded $n$-cell systems are reported. It is shown that for…
We characterize the Hermite-Biehler (de Branges) functions $E$ which correspond to Shroedinger operators with $L^2$ potential on the finite interval. From this characterization one can easily deduce a recent theorem by Horvath. We also…
We consider the eigenvalue equation for the Laplace-Beltrami operator acting on scalar functions on the non-compact Eguchi-Hanson space. The corresponding differential equation is reducible to a confluent Heun equation with Ince symbol…
A method for the computation of scattering data and of the Green function for the one-dimensional Schr\"{o}dinger operator $H:=-\frac{d^2}{dx^2}+q(x)$ with a decaying potential is presented. It is based on representations for the Jost…
The Schr\"odinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have…
Let (M,g) be a n-dimensional compact Riemannian manifold. We consider the magnetic deformations of semiclassical Schrodinger operators on M for a family of magnetic potentials that depends smoothly on $k$ parameters $u$, for $k \geq n$, and…
We define functions of noncommuting self-adjoint operators with the help of double operator integrals. We are studying the problem to find conditions on a function $f$ on ${\Bbb R}^2$, for which the map $(A,B)\mapsto f(A,B)$ is Lipschitz in…
This work provides an introduction and overview on some basic mathematical aspects of the single-flux Aharonov-Bohm Schr\"odinger operator. The whole family of admissible self-adjoint realizations is characterized by means of four different…
We study the spectral zeta functions associated to the radial Schr\"odinger problem with potential V(x)=x^{2M}+alpha x^{M-1}+(lambda^2-1/4)/x^2. Using the quantum Wronskian equation, we provide results such as closed-form evaluations for…
We give a fully explicit description of Lie algebra derivatives (generalizing raising and lowering operators) for representations of SL(3,R) in terms of a basis of Wigner functions. This basis is natural from the point of view of principal…
Self-adjoint Schr\"odinger operators with $\delta$ and $\delta'$-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity…
The Lieb-Liniger model which has a weak external potential term under the periodic boundary condition is investigated. By exploiting the Bethe states as bases, we perform a perturbation analysis up to the first order to obtain the shifts of…
This paper addresses particular eigenvalue problems within the context of two quaternionic function theories. More precisely, we study two concrete classes of quaternionic eigenvalue problems, the first one for the slice derivative operator…
We present a new six-parameter family of potentials whose solutions are expressed in terms of the hypergeometric functions 3F2, 2F2 and 1F2. Both the scattering data and the bound states of these potentials are explicitly computed and the…
We present a perturbative construction of two kinds of eigenfunctions of the commuting family of difference operators defining the elliptic Ruijsenaars system. The first kind corresponds to elliptic deformations of the Macdonald…
We study Schr\"odinger operators on $\mathbb{R}^2$ $$ H = \left(-\frac{\partial^2}{\partial x_1^2}\right)^{\alpha/2} + \left(-\frac{\partial^2}{\partial x_2^2}\right)^{\alpha/2} + V, $$ for $\alpha \in (0,2)$ and some sufficiently regular,…
We find that the quantum monodromy matrix associated with a derivative nonlinear Schrodinger (DNLS) model exhibits U(2) or U(1,1) symmetry depending on the sign of the related coupling constant. By using a variant of quantum inverse…
The article is devoted to the following question. Consider a periodic self-adjoint difference (differential) operator on a graph (quantum graph) G with a co-compact free action of the integer lattice Z^n. It is known that a local…
I present an example of a discrete Schr"odinger operator that shows that it is possible to have embedded singular spectrum and, at the same time, discrete eigenvalues that approach the edges of the essential spectrum (much) faster than…
We present an analytical investigation of the asymptotic behavior of non-resonance eigenvalues for the fractional Schr\"odinger operator under homogeneous Neumann boundary conditions. Our findings reveal an intriguing convergence: as the…