Related papers: Time asymptotics of the Schroedinger wave function…
Under the effect of suitable time-periodic magnetic fields, the velocity of a charged particle grows exponentially in $t$; this phenomenon provides the asymptotic completeness for wave operators with slowly decaying potentials. These facts…
We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric variation. We show that for generic forcing which includes…
We analyze the time evolution of a one-dimensional quantum system with zero range potential under time periodic parametric perturbation of arbitrary strength and frequency. We show that the projection of the wave function on the bound state…
We consider the two dimensional Schr\"odinger equation with time dependent delta potential, which represents a model for the dynamics of a quantum particle subject to a point interaction whose strength varies in time. First, we prove global…
We present rigorous results for quantum systems with both bound and continuum states subjected to an arbitrary strength time-periodic field. We prove that the wave function takes the form of a sum of time-periodic resonant states with…
For $N$-body Schr\"o\-dinger operators with time-periodic short-range pair-potentials we show by a time-dependent commutator method that all channel wave operators exist. For $N=2$ we prove asymptotic completeness by a simplified version of…
We consider the Schr\"odinger equation with a time-independent weakly random potential of a strength $\epsilon\ll 1$, with Gaussian statistics. We prove that when the initial condition varies on a scale much larger than the correlation…
We consider the Schroedinger equation with a general interaction term, which is localized in space. The interaction may be x, t dependent and non-linear. Purely non-linear parts of the interaction are localized via the radial Sobolev…
We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric variation $\eta(t)$. We show that for generic $\eta(t)$,…
We analyze the long time behavior of solutions of the Schr\"odinger equation $i\psi_t=(-\Delta-b/r+V(t,x))\psi$, $x\in\RR^3$, $r=|x|$, describing a Coulomb system subjected to a spatially compactly supported time periodic potential…
The transient diffusion-limited current at a disk electrode following a change in interfacial ion concentration induced by a potential step is analyzed with direct relevance to chronoamperometric measurements. The mixed-boundary diffusion…
In this contribution we present an overview of our work on the numerical simulation of the perturbation of a black hole space-time by incoming gravitational waves. The formulation we use is based on Friedrich's general conformal equations…
We consider wave dynamics for a Schr\"odinger equation with a non-Hermitian Hamiltonian $\mathcal{H}$ satisfying the generalized (anyonic) parity-time symmetry $\mathcal{PT H}= \exp(2 i \varphi) \mathcal{HPT}$, where $\mathcal{P}$ and $…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
For the Schr\"odinger equation with a general interaction term, which may be linear or nonlinear, time dependent and including charge transfer potentials, we prove the global solutions are asymptotically given by the sum of a free wave and…
We study localization effects of disorder on the spectral and dynamical properties of Schroedinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection…
We show that the standard Dirac phase factor is not the only solution of the gauge transformation equations. The full form of a general gauge function (that connects systems that move in different sets of scalar and vector potentials),…
There is much discussion in the mathematical physics literature as well as in quantum mechanics textbooks on spherically symmetric potentials. Nevertheless, there is no consensus about the behavior of the radial function at the origin,…
We study the solutions of linear Schroedinger equations in which the potential energy is a periodic function of time and is sufficiently localized in space. We consider the potential to be close to one that is time periodic and yet…
It has been found a simple procedure for the general solution of the time-independent Schr\"odinger equation (SE) with the help of quantization of potential area in one dimension without making any approximation. Energy values are not…