Related papers: Two-dimensional von Neumann--Wigner potentials wit…
We study sufficient conditions for the absence of positive eigenvalues of magnetic Schr\"odinger operators in $\mathbb{R}^d,\, d\geq 2$. In our main result we prove the absence of eigenvalues above certain threshold energy which depends…
It is proven that the absolutely continuous spectrum of matrix Schr\"{o}dinger operators coincides (with the multiplicity taken into account) with the spectrum of the unperturbed operator if the (matrix) potential is square integrable. The…
The Darboux transformation operator technique in differential and integral forms is applied to the generalized Schrodinger equation with a position-dependent effective mass and with linearly energy-dependent potentials. Intertwining…
We prove essential self-adjointness for semi-bounded below magnetic Schr\"odinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. Some singularities of the scalar…
For $a \ge - {( \frac{{d}}{2}- 1)^2} $ and $2\sigma= {{d - 2}}-( {{{(d - 2)}^2} + 4a})^{1/2}$, let $$\begin{cases}\mathcal{H}_{a}= - \Delta + \frac{a} {{{{ | x |}^2}}},\\ \mathcal{\widetilde{H}}_{\sigma}= 2\big( { - \Delta + \frac{{{\sigma…
This paper presents a thorough analysis of 1-dimensional Schroedinger operators whose potential is a linear combination of the Coulomb term 1/r and the centrifugal term 1/r^2. We allow both coupling constants to be complex. Using natural…
We apply a simple transformation method to construct a set of new exactly solvable potentials (ESP) which gives rise to bound state solution of $D$-dimensional Schr\"odinger equation. The important property of such exactly solvable quantum…
We show that at least the quasi-exactly solvable eigenvalues of the Schr\"odinger equation with the potential $V(x) = -(\zeta \cosh 2x -iM)^2$ as well as the periodic potential $V(x) = (\zeta \cos 2\theta -iM)^2$ are real for the…
In the framework of the resolvent approach it is introduced a so called twisting operator that is able, at the same time, to superimpose \`a la Darboux $N$ solitons to a generic smooth decaying potential of the Nonstationary Schr\"odinger…
We refine a method for finding a canonical form for symmetry operators of arbitrary order for the Schroedinger eigenvalue equation on any 2D Riemannian manifold, real or complex, that admits a separation of variables in some orthogonal…
In a recent contribution we showed that there exists a smooth, dense domain for singular potential Schr\"odinger operators on the real line which is invariant under taking derivatives of arbitrary order and under multiplication by positive…
Irreducible second-order Darboux transformations are applied to the periodic Schrodinger's operators. It is shown that for the pairs of factorization energies inside of the same forbidden band they can create new non-singular potentials…
It is shown that the 1-dimensional lattice Schrodinger operator with potential given by a non-zero multiple of the Moebius function has positive Lyapounov exponent. In view of the classical theory of random Schrodinger operators, this may…
Using the coordinate transformation method, we solve the one-dimensional Schr\"{o}dinger equation with position-dependent mass(PDM). The explicit expressions for the potentials, energy eigenvalues and eigenfunctions of the systems are…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
We prove a Wegner estimate for discrete Schr\"odinger operators with a potential given by a Gaussian random process. The only assumption is that the covariance function decays exponentially, no monotonicity assumption is required. This…
We prove that the eigenvalues of a continuum random Schr\"odinger operator $-\Delta+ V_{\omega}$ of Anderson type, with complex decaying potential, can be bounded (with high probability) in terms of an $L^q$ norm of the potential for all…
We introduce a weighted de Rham operator which acts on arbitrary tensor fields by considering their structure as r-fold forms. We can thereby define associated superpotentials for all tensor fields in all dimensions and, from any of these…
We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large distance. We show that this operator possesses a sequence of…
We consider the problem of estimating the eigenvalues and the integral of the corresponding eigenfunctions, associated to the Newtonian potential operator, defined in a bounded domain $\Omega \subset \mathbb{R}^{d},$ where $d = 2, 3$, in…