Related papers: Re-Thinking Schroedinger Boundary Conditions: the …
The Laplace transform is a valuable tool in physics, particularly in solving differential equations with initial or boundary conditions. A 2014 study by Tsaur and Wang (2014 \emph{Eur.~J.~Phys.} \textbf{35} 015006) introduced a…
We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential…
Random boundary conditions are one of the simplest realizations of quenched disorder. They have been used as an illustration of various conceptual issues in the theory of disordered spin systems. Here we review some of these results.
We present and exploit an analogy between lack of absolutely continuous spectrum for Schroedinger operators and natural boundaries for power series. Among our new results are generalizations of Hecke's example and natural boundary examples…
It is shown that a large subset of initial data with finite energy ($L^2$ norm)evolves nearly linearly in nonlinear Schr\" odinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such…
Following Symanzik we argue that the Schr\"odinger functional in lattice gauge theories without matter fields has a well-defined continuum limit. Due to gauge invariance no extra counter terms are required. The Schr\"odinger functional is,…
The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a second moment, it is…
We investigate Luttinger junctions of quantum wires away from criticality. The one-body scattering matrix, corresponding to the off-critical boundary conditions at the junction, admits in general antibound and/or bound states. Their…
By using the multipolar gauge it is shown that the quantum mechanics of an electrically charged particle moving in a prescribed classical electromagnetic field (wave mechanics) may be expressed in a manner that is gauge invariant, except…
We consider the problem of constructing transparent boundary conditions for the time-dependent Schr\"odinger equation with a compactly supported binding potential and, if desired, a spatially uniform, time-dependent electromagnetic vector…
By assuming that the kinetic energy,potential energy,momentum,and some other physical quantities of a particle exist in the field out of the particle,the Schrodinger equation is an equation describing field of a particle,but not the…
We consider the matrix-valued Schr\"odinger operator on the half line with the general selfadjoint boundary condition. When the discrete spectrum is changed without changing the continuous spectrum, we present a review of the…
In classical external gauge fields that fall off less fast than the inverse of the evolution parameter (time) of the system the implementability of a unitary perturbative scattering operator ($S$-matrix) is not guaranteed, although the…
This note points out some bounds for the number of negative eigenvalues of Schroedinger operators with Hardy-type potentials, which follow from a simple coordinate transformation, and could prove useful in a spectral analysis of certain…
We describe the behaviour of semiclassical electrodynamics under gauge transformations. For this purpose we observe the structure of Schr\"odinger equation and matricial elements under these transformations. We conclude this theory is not…
Even though its classical equations of motion are then left invariant, when an action is redefined by an additive total derivative or divergence term (in time, in the case of a mechanical system) such a transformation induces nontrivial…
The one-dimensional Schr\"odinger equation with the point potential in the form of the derivative of Dirac's delta function, $\lambda \delta'(x)$ with $\lambda$ being a coupling constant, is investigated. This equation is known to require…
We describe inverse scattering for the matrix Schroedinger operator with general selfadjoint boundary conditions at the origin using the Marchenko equation. Our approach allows the recovery of the potential as well as the boundary…
Schroedinger developed an operator method for solving quantum mechanics. While this technique is overshadowed by his more familiar differential equation approach, it has found wide application as an illustration of supersymmetric quantum…
We consider the eigenvalue problem for the Schr\"odinger operator on bounded, convex domains with mixed boundary conditions, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its…