Related papers: Fundamental solutions for Schrodinger operators w…

Fundamental solution for a Schr\"odinger equation with a time-dependent potential of long-range type is constructed. The solution is given as a Fourier integral operator with a symbol uniformly bounded global in time, when measured in…

Positivity, essential self-adjointness, and spectral properties of a class of Schroedinger operators with multipolar inverse-square potentials are discussed. In particular a necessary and sufficient condition on the masses of singularities…

In this paper we will study the existence of fundamental solutions for the explicit and implicit backward time dependent Schodinger equation, via discrete Fourier transform and its symbol for the Laplace operator. In both cases we will…

We discuss 1-dimensional Schrodinger operators with complex and locally integrable potentials that may have an arbitrary behavior at (finite or infinite) endpoints. The main tool of our analysis are Green's operators, that is, their various…

We prove that the inverse scattering problem for the Schr\"odinger operator with the separable potential can be reduced to the solving of a certain singular integral equation. We establish the uniqueness of the potential corresponding to…

We consider the unitary group for the Schr\"odinger operator with inverse-square potential. We adapt Combes-Thomas estimates to show that, when restricted to non-radial functions, the operator enjoys much better estimates that mirror those…

In this note we solve theoretically the Schrodingers differential equation using results based on our previous work which concern semigroup operators. Our method does not use eigenvectors or eigenvalues and the solution depends only from…

In this note we give explicit solutions to the wave equation associated to the Schr\"odinger operator with three-inverse square potential on $R_+^3$

We study positivity, localization of binding and essential self-adjointness properties of a class of Schroedinger operators with many anisotropic inverse square singularities, including the case of multiple dipole potentials.

We study the uniform resolvent estimates for Schr\"odinger operator with a Hardy-type singular potential. Let $\mathcal{L}_V=-\Delta+V(x)$ where $\Delta$ is the usual Laplacian on $\mathbb{R}^n$ and $V(x)=V_0(\theta) r^{-2}$ where $r=|x|,…

In this paper we study a generalization of the classical Rarita-Schwinger type operators and construct their fundamental solutions. We give some basic integral formulas related to these operators. We also establish that the projection…

Let P be the operator $-\Delta+V$ on R^d, where $V$ is a real potential with several inverse square singularities. The usual non-trapping type high-frequency inequality on the truncated resolvent of $P$ is shown, using semi-classical…

In this work we give explicit formulas for the Schwartz integral kernels of some multipliers of the Schr\"odinger operator with inverse square potential on $\R^\ast_+$. By using the integral transforms connecting these multipliers we obtain…

We give a complete characterisation of the reflectionless Schr\"odinger operators on the line with integrable potentials, solve the inverse scattering problem of reconstructing such potentials from the eigenvalues and norming constants, and…

Following [D,BDG,DR], I describe several exactly solvable families of closed operators. Some of these families are defined by the theory of singular rank one perturbations. The remaining families are Schrodinger operators with inverse…

We study a class of logarithmic Schrodinger equations with periodic potential which come from physically relevant situations and obtain the existence of infinitely many geometrically distinct solutions.

We establish that the potential appearing in a fractional Schr\"odinger operator is uniquely determined by an internal spectral data.

The norm resolvent convergence of a family of one-dimensional Schroedinger operators with singular magnetic and electric potentials of small support is studied.

We develop direct and inverse scattering theory for one-dimensional Schroedinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete…

We study one-dimensional Schr\"{o}dinger operators $\mathrm{S}(q)$ on the space $L^{2}(\mathbb{R})$ with potentials $q$ being complex-valued generalized functions from the negative space $H_{unif}^{-1}(\mathbb{R})$. Particularly the class…