Related papers: Structure formulas for wave operators
For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…
The present contribution contains a quite extensive theory for the stability analysis of plane periodic waves of general Schr{\"o}dinger equations. On one hand, we put the one-dimensional theory, or in other words the stability theory for…
We review some of the literature on intertwining wave operators, as far as it relates to Tosio Kato's stationary method based on the resolvent. Techniques from Fourier restriction and Wiener algebras are emphasized.
In this paper we constructively determine a family of the spectral invariants of the multidimensional Schrodinger operator with a periodic potential by the given band functions.
The purpose of this paper is to give some refined results about the distribution of resonances in potential scattering. We use techniques and results from one and several complex variables, including properties of functions of completely…
The notion of the wave spectrum of a semi-bounded symmetric operator was introduced by one of the authors in 2013. The wave spectrum is a topological space determined by the operator in a canonical way. The definition uses a dynamical…
We prove a general Levinson's theorem for Schr\"odinger operators in two dimensions with threshold obstructions at zero energy. Our results confirm and simplify earlier seminal results of Boll\'e, Gesztesy et al., while providing an…
Starting on the basis of $q$-symmetric oscillator algebra and on the associate $q$-calculus properties, we study a deformed quantum mechanics defined in the framework of the basic square-integrable wave functions space. In this context, we…
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…
Here we have studied first and second-order intertwining approach to generate isospectral partner potentials of position-dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as…
This paper describes the results from a numerical estimation of the force exerted by long surface waves on a fixed and partially immersed rectangular structure. The topic is connected with the need of making decisions on the design,…
The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account…
We establish a semi-classical formula for the sum of eigenvalues of a magnetic Schrodinger operator in a three-dimensional domain with compact smooth boundary and Neumann boundary conditions. The eigenvalues we consider have eigenfunctions…
We consider inverse dynamical, spectral, quantum and acoustical scattering problems for the Schr\"odinger operator on the half line. The goal of the paper is to establish the connections between different types of inverse data for these…
The position operator (defined within the Schroedinger representation in the standard way) becomes meaningless when periodic boundary conditions are adopted for the wavefunction, as usual in condensed matter physics. We show how to define…
We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…
In this paper, we prove existence and orbital stability results of periodic standing waves for the cubic-quintic nonlinear Schr\"odinger equation. We use the implicit function theorem to construct a smooth curve of explicit periodic waves…
The continuity property in the Sobolev space $W^{k,p}({\bf R}^m)$ of wave operators of scattering theory for $m$-dimensional single-body Schr\"odinger operator is considered when the resolvent of the operator has singularities at the bottom…
We consider the Schroedinger operator in R^3 with N point interactions placed at Y=(y_1, ... ,y_N), y_j in R^3, of strength a=(a_1, ... ,a_N). Exploiting the spectral theorem and the rather explicit expression for the resolvent we prove a…
We consider a simple modification of the 1D-Laplacian where non-mixed interface conditions occur at the boundaries of a finite interval. It has recently been shown that Schr\"odinger operators having this form allow a new approach to the…