Related papers: Characterization of the ranges of wave operators f…
In this paper, we consider the existence and the asymptotic completeness of the wave operators for Schrodinger equations with time-dependent potentials which are short-range in space.
In this paper, we construct a modified wave operators for Schrodinger equations with time-dependent long-range potentials by using wave packet transform and give a proof of the existence of the modified wave operators.
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…
We construct time-dependent wave operators for Schr\"{o}dinger equations with long-range potentials on a manifold $M$ with asymptotically conic structure. We use the two space scattering theory formalism, and a reference operator on a space…
We present a program to simulate the dynamics of a wave packet interacting with a time-dependent potential. The time-dependent Schr\"odinger equation is solved on a one-, two-, or three-dimensional spatial grid using the split operator…
We provide a simple sufficient condition in an abstract framework to deduce the existence and completeness of wave operators (resp. modified wave operators) on Sobolev spaces from the existence and completeness of the usual wave operators…
This paper establishes the $L^p$ boundedness of wave operators for linear Schr\"odinger equations in $\mathbb{R}^3$ with time-dependent potentials. The approach to the proof is based on new cancellation lemmas. As a typical application…
The solution of the Schrodinger equation with a linear potential is considered. We use algebraic methods to obtain the explicit form of the solution for the explicitly time dependent Hamiltonian and discuss the general conditions which…
We prove existence of modified wave operators for one-dimensional Schr\"odinger equations with potential in $L^p(\reals)$, $p<2$. If in addition the potential is conditionally integrable, then the usual M\"oller wave operators exist. We…
We argue that the way to get the general solution of a Schrodinger equation in the presence of a time-dependent linear potential based on the Lewis-Riesenfeld framework is to use a Hermitian linear invariant operator. We demonstrate that…
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…
An explicit formula for the wave operators associated with Schroedinger operators on the discrete half-line is deduced from their stationary expressions. The formula enables us to understand the wave operators as one dimensional…
We prove that the wave operators for $n \times n$ matrix Schr\"odinger equations on the half line, with general selfadjoint boundary condition, are bounded in the spaces $L^p(\mathbb R^+, \mathbb C^n), 1 < p < \infty, $ for slowly decaying…
We derive an exact analytical solution to the time-dependent Schr\"odinger equation for transmission of a Gaussian wave packet through an arbitrary potential of finite range. We consider the situation where the initial Gaussian wave packet…
In this paper, we define time-independent modifiers to construct a long-range scattering theory for discrete schr\"odinger operators on the square lattice $\mathbb{Z}^N$. We prove the existence and completeness of modified wave operators in…
In this paper, we determine the wave front set of solutions to the Schr\"{o}dinger equation with time-dependent magnetic fields. We considered time-dependent and `not so small' magnetic fields through the method using the wave packet…
We consider Schr\"odinger operators $H$ on $R^n$ with variable coefficients. Let $H_0=-\frac12\triangle$ be the free Schr\"odinger operator and we suppose $H$ is a "short-range" perturbation of $H_0$. Then, under the nontrapping condition,…
We give another proof of the $L^p$ boundedness of scattering wave operators, at the low frequency part of the data. The proof also allows the control of the commutator of multiplication by $|x|$ with the wave operator in $L^p$. The method…
In this paper, we study the linear and nonlinear Schr\"odinger equations with a time-decaying harmonic oscillator and inverse-square potential. This model retains a form of scale invariance, and using this property, we demonstrate the…
We construct a time-dependent scattering theory for Schr\"odinger operators on a manifold $M$ with asymptotically conic structure. We use the two-space scattering theory formalism, and a reference operator on a space of the form $R\times…