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The convergence problem for scattering states is studied in detail within the framework of the Algebraic Model, a representation of the Schrodinger equation in an L^2 basis. The dynamical equations of this model are reformulated featuring…
In this article, we determine the wave front sets of solutions to time dependent Schr\"odinger equations with a sub-quadratic potential by using the representation of the Schr\"dingier evolution operator via wave packet transform (short…
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite…
In the framework of the application of the Boundary Control method to solving the inverse dynamical problems for the one-dimensional Schr\"odinger and Dirac operators on the half-line and semi-infinite discrete Schr\"odinger operator, we…
Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in atomic, nuclear and particle physics,…
We consider the spectrum of a Schroedinger operator in a multi-dimensional cylinder perturbed by a shrinking potential. We study the phenomenon of a new eigenvalue emerging from the threshold of the essential spectrum and give the…
For small-amplitude semilinear wave equations with power type nonlinearity on the first-order spatial derivative, the expected sharp upper bound on the lifespan of solutions is obtained for both critical cases and subcritical cases, for all…
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…
We provide bounds on the error between dynamics of an infinite dimensional bilinear Schr\"odinger equation and of its finite dimensional Galerkin approximations. Standard averaging methods are used on the finite dimensional approximations…
This work deals with Schr\"odinger equations with quadratic and sub-quadratic Hamiltonians perturbed by a potential. In particular we shall focus on bounded, but not necessarily smooth perturbations. We shall give a representation of such…
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…
The particle in an expanding/contracting 1-dimension box is revisited in action-angle like variables with direct thermodynamic interpretation. An angle dependent potential is proposed accurately describing the mechanical behavior while also…
We demonstrate, for the first time, that neural scaling laws can deliver near-exact solutions to the many-electron Schr\"odinger equation across a broad range of realistic molecules. This progress is enabled by the Lookahead Variational…
We establish Lieb-Thirring type inequalities for non self-adjoint relatively compact perturbations of certain operators of mathematical physics. We apply our results to quantum Hamiltonians of Schr{\"o}dinger and Pauli with constant…
We analyze the behavior of the energy spectrum of the Klein-Gordon equation in the presence of a truncated hyperbolic tangent potential. From our analysis we obtain that, for some values of the potential there is embedding of the bound…
We study quantum transport for the discrete one-dimensional random Jacobi operator of divergence-gradient type. For strictly positive and bounded random variables, we analyze the q-moments of the position operator and establish both upper…
Variational solutions of the Boltzmann equation usually rely on the concept of linear response. We extend the variational approach for tight-binding models at high entropies to a regime far beyond linear response. We analyze both weakly…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…
We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An…