Related papers: The initial-to-final-state inverse problem with cr…
In this paper we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a…
This paper presents an optimization approach to explain why and how a quantum system evolves from an arbitrary initial state to a stationary state, satisfying the time-independent Schr\"{o}dinger equation. It also points out the inaccuracy…
We consider the problem of steering a linear stochastic system between two end-point degenerate Gaussian distributions in finite time. This accounts for those situations in which some but not all of the state entries are uncertain at the…
We consider Schr\"odinger operators on [0,\infty) with compactly supported, possibly complex-valued potentials in L^1([0,\infty)). It is known (at least in the case of a real-valued potential) that the location of eigenvalues and resonances…
We study the time-dependent Schr\"odinger operator $P = D_t + \Delta_g + V$ acting on functions defined on $\mathbb{R}^{n+1}$, where, using coordinates $z \in \mathbb{R}^n$ and $t \in \mathbb{R}$, $D_t$ denotes $-i \partial_t$, $\Delta_g$…
The manuscript is concerned with uniqueness and stability for inverse source problem of determining spatially varying factor $f(x)$ of a source term given by $R(t)f(x)$ with suitable given $R(t)$ in the right hand side of the Schr\"odinger…
We prove unique continuation principles for solutions of evolution Schr\"odinger equations with time dependent potentials. These correspond to uncertainly principles of Paley-Wiener type for the Fourier transform. Our results extends to a…
We consider the inverse coefficient problem of simultaneously determining the space dependent electromagnetic potential, the zero-th order coupling term and the first order coupling vector of a two-state Schr\"odinger equation in a bounded…
We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain from one boundary Neumann observation of the solution. We prove H\"older stability…
We prove that the solutions to the initial-value problem for 2-dimensional Schr\"odinger maps are unique in $C_tL_x^{\infty} \cap L_t^{\infty} (\dot{H}^1_x\cap \dot{H}^2_x)$. For the proof, we follow McGahagan's argument with improving its…
In this work, we construct time-dependent potentials for the Schr\"odinger equation via supersymmetric quantum mechanics. The generated potentials have a quantum state with the property that after a particular threshold time $t_F$, when the…
I investigate spacetime singularities from the point of view of the wavefunction of the universe. In order to extend the classical notion of geodesic incompleteness one has to include the proper time of an observer as a degree of freedom in…
We study an initial value problem for the one-dimensional non-stationary linear Schr\"odinger equation with a point singular potential. In our approach, the problem is considered as a system of coupled initial-boundary value (IBV) problems…
We consider d-dimensional time dependent Schr\"odinger equations on the Hilbert space of square integrable functions. We assume magnetic and scalar potentials are almost critically singular with respect to spatial variables both locally and…
We prove that an $L^\infty$ potential in the Schr\"odinger equation in three and higher dimensions can be uniquely determined from a finite number of boundary measurements, provided it belongs to a known finite dimensional subspace…
The purpose of the present paper is to discuss the time dependent Schr\"odinger equation on a metric graph with time-dependent edge lengths, and the proper way to pose the problem so that the corresponding time evolution is unitary. We show…
We consider, on a trivial vector bundle over a Riemannian manifold with boundary, the inverse problem of uniquely recovering time- and space-dependent coefficients of the dynamic, vector-valued Schr\"odinger equation from the knowledge of…
This result will be published as part of my PhD thesis after some streamlining. This manuscript contains the proof of the claim, but is not peer-reviewed. We prove uniqueness and stability for the inverse problem of the 2D Schr\"odinger…
We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial…
We prove unique continuation properties for linear variable coefficient Schr\"odinger equations with bounded real potentials. Under certain smallness conditions on the leading coefficients, we prove that solutions decaying faster than any…