5 papers · 1 filter
Stability estimates for the initial-to-final-state inverse problem
Manuel Cañizares, Thanasis Zacharopoulos
The initial-to-final-state inverse problem for the Schrödinger equation consists in determining uniquely the Hamiltonian that generates the evolution, assuming the knowledge of the…
The initial-to-final-state inverse problem with critically-singular potentials
Manuel Cañizares, Pedro Caro, Ioannis Parissis +1
The Schrödinger equation in high dimensions describes the evolution of a quantum system. Assume that we are given the evolution map sending each initial state $f\in L^2(\mathbb{R}^…
The initial-to-final-state inverse problem with time-independent potentials
Manuel Cañizares, Pedro Caro, Ioannis Parissis +1
The initial-to-final-state inverse problem consists in determining a quantum Hamiltonian assuming the knowledge of the state of the system at some fixed time, for every initial sta…
Boundary deformation techniques for Neumann problems for the Helmholtz equation
Manuel Cañizares
We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the depend…
Local near-field scattering data enables unique reconstruction of rough electric potentials
Manuel Cañizares
The focus of this paper is the study of the inverse point-source scattering problem, specifically in relation to a certain class of electric potentials. Our research provides a nov…