Related papers: Fundamental solutions for Schrodinger operators w…

The Schr\" odinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring…

We study Schr\"odinger operators given by positive quadratic forms on infinite graphs. From there, we develop a criticality theory for Schr\"odinger operators on general weighted graphs.

An explicit formula is given for a fundamental solution for a class of semielliptic operators. The fundamental solution is used to investigate properties of these operators as mappings between weighted function spaces. Necessary and…

Here we define Rarita-Schwinger operators on cylinders and construct their fundamental solutions. Further the fundamental solutions to the cylindrical Rarita-Schwinger type operators are achieved by applying translation groups. In turn, a…

We outline a general method of obtaining exact solutions of Schroedinger equations with a position dependent effective mass. Exact solutions of several potentials including shape invariant potentials have also been obtained.

This study presents the solutions of Schr\"odinger equation for the Non-Central Generalized Inverse Quadratic Yukawa Potential within the framework of Nikiforov-Uvarov. The radial and angular part of the Schr\"odinger equation are obtained…

We show that the resonance counting function for a Schr\"odinger operator has maximal order of growth for generic sets of real-valued, or complex-valued, $L^\infty$-compactly supported potentials.

In this paper we investigate the existence of positive solutions and ground state solution for a class of fractional Schr\"odinger-Poisson equations in $\mathbb R^3$ with general nonlinearities.

We give an explicit formula for the wave operators for Schroedinger operators on the half-line with a potential decaying strictly faster than the polynomial of degree minus two. The formula consists of the main term given by the scattering…

We solve the one-dimensional Schr\"odinger equation for the bound states of two potential models with a rich structure as shown by their "spectral phase diagram". These potentials do not belong to the well-known class of exactly solvable…

Utilizing an ${\it ansatz}$ for the eigenfunctions, we arrive at an exact closed form solution to the Schr\"{o}dinger equation with the inverse-power potential, $V(r)=ar^{-4}+br^{-3}+cr^{-2}+dr^{-1}$ in two dimensions, where the parameters…

Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where $\Delta $ is the Laplacian operator on $\rz$, while nonnegative potential $V$ belongs to the reverse H\"{o}lder class. In this paper, we establish the weighted norm inequalities for…

We obtain a reverse H\"older inequality for the eigenfuctions of the Schr\"odinger operator with slowly decaying potentials. The class of potentials includes singular potentials which decay like $|x|^{-\alpha}$ with $0<\alpha<2$, in…

Using an extension of the H\"ormander product of distributions, we obtain an intrinsic formulation of one-dimensional Schr\"odinger operators with singular potentials. This formulation is entirely defined in terms of standard {\it Schwartz}…

For one-dimensional Schroedinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. Our (non-semi-classical) approach results in substantial progress in achieving optimal conditions…

We review an exact WKB resolution method for the stationary 1D Schr\"odinger equation with a general polynomial potential. This contribution covers already published material: we supply a commented summary here, stressing a few aspects…

We construct solutions to the eikonal equation for a class of long-range potentials, derive strong radiation condition bounds for the corresponding Schr\"odinger operator and apply them to construct the generalized Fourier transform,…

In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schr\"odinger operators whose potentials are obtained by real-valued sampling along the orbits of an ergodic invertible transformation. After an…

An inverse problem is considered for an inhomogeneous Schr\"odinger equation. Assuming that the potential vanishes outside a finite interval and satisfies some other technical assumptions, one proves the uniqueness of the recovery of this…

In this paper the complete spectral analysis of the operators is carried out and also with help of generalized normalizing numbers the inverse problem is solved.