Related papers: Unique continuation for the Schrodinger equation w…
We prove Strichartz-type estimates for Schroedinger's equation with time-dependent potentials. The time derivative of the potentials need not be integrable, so the total variation of the potentials may be infinite.
We investigate unique continuation inequalities for solutions of the Schr\"odinger equations associated with special Hermite operators. Our main result establishes that if the solution remains small at two distinct time points outside sets…
In this paper we study unique continuation theorems for magnetic Schr\"odinger equation via Carleman estimates. We use integration by parts techniques in order to show these estimates. We consider electric and magnetic potentials with…
A variational technique is established to deal with the Schrodinger equation with parity-time(PT) symmetric Gaussian complex potential. The method is extended to the linear and self-focusing and defocusing nonlinear cases. Some unusual…
We prove that if a solution of the time-dependent Schr{\"o}dinger equation on an homogeneous tree with bounded potential decays fast at two distinct times then the solution is trivial. For the free Schr{\"o}dinger operator, we use the…
We present a simple and self-contained approach to establish the unique continuation property for some classical evolution equations of second order in a cylindrical domain. We namely discuss this property for wave, parabolic and…
The linear Schr\"odinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum mechanics and shares many qualitative features with…
This paper establishes new estimates for linear Schroedinger equations in R^3 with time-dependent potentials. Some of the results are new even in the time-independent case and all are shown to hold for potentials in scaling-critical,…
The outlook of a simple method to generate localized (soliton-like) potentials of time-dependent Schrodinger type equations is given. The conditions are discussed for the potentials to be real and nonsingular. For the derivative Schrodinger…
In this paper, Hardy's uncertainty principle and unique continuation properties of abstract Schr\"odinger equations in vector-valued classes are obtained
We relax the regularity condition on potentials of the Schr\"odinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].
We establish a unique continuation property for stochastic heat equations evolving in a bounded domain $G$. Our result shows that the value of the solution can be determined uniquely by means of its value on an arbitrary open subdomain of…
We construct a local in time, exponentially decaying solution of the one-dimensional variable coefficient Schrodinger equation by solving a nonstandard boundary value problem. A main ingredient in the proof is a new commutator estimate…
In this paper, we give estimates of the solutions to Schr\"{o}dinger equation on modulation spaces with vector potential of sub-linear growth.
In this paper, we extend our earlier unique continuation results \cite{PZ2} for the Schr\"odinger-type inequality $ |\bar\partial u| \le V|u|$ on a domain in $\mathbb C^n$ by removing the smoothness assumption on solutions $u = (u_1,…
An algorithm for the numerical solution of the Schr\"odinger equation in the case of a time dependent potential is proposed. Our simple modification upgrades the well known method of Koonin while negligibly increasing the computing time. In…
The unique-continuation property from sets of positive measure is here proven for the many-body magnetic Schr\"odinger equation. This property guarantees that if a solution of the Schr\"odinger equation vanishes on a set of positive…
We find exact solutions of the time-dependent Schr\"odinger equation for a family of quasi-exactly solvable time-dependent potentials by means of non-unitary gauge transformations.
We consider the relativistic Schr\"odinger equation with a time dependent vector and scalar potential on a bounded cylindrical domain. Using a Geometric Optics Ansatz we establish a logarithmic stability estimate for the recovery of the…
In this note we study the property of unique continuation for solutions of $|(-\Delta)^{\alpha/2}u|\leq|Vu|$, where $V$ is in a function class of potentials including $\bigcup_{p>n/\alpha}L^p(\mathbb{R}^n)$ for $n-1\leq\alpha<n$. In…