Related papers: Inverse Quantum Potential Reconstruction via Gener…
This article develops the numerical and theoretical study of a reconstruction algorithm of a potential in a wave equation from boundary measurements, using a cost functional built on weighted energy terms coming from a Carleman estimate.…
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the…
The inverse problem of estimating dielectric constants of explosives using boundary measurements of one component of the scattered electric field is addressed. It is formulated as a coefficient inverse problem for a hyperbolic differential…
We are concerned with inverse boundary problems for first order perturbations of the Laplacian, which arise as model operators in the acoustic tomography of a moving fluid. We show that the knowledge of the Dirichlet--to--Neumann map on the…
Reconstructing spectral densities from Euclidean lattice correlators requires an inverse Laplace transform, which is inherently ill-conditioned when applied to numerical data with statistical uncertainties. The maximum amount of information…
Unoriented surface reconstructions based on the Gauss formula have attracted much attention due to their elegant mathematical formulation and excellent performance. However, the isotropic characteristics of the formulation limit their…
The primary objective of this research is to investigate an inverse problem of parameter identification in nonlinear mixed quasi-variational inequalities posed in a Banach space setting. By using a fixed point theorem, we explore properties…
Inverse problems arising in (geo)magnetism are typically ill-posed, in particular {they exhibit non-uniqueness}. Nevertheless, there exist nontrivial model spaces on which the problem is uniquely solvable. Our goal is here to describe such…
A relation between the deformed Hulth\'en potential and the Eckart one is used to write the bound-state wavefunctions of the former in terms of Jacobi polynomials and to calculate their normalization coefficients. The shape invariance…
The inverse scattering problem of the reconstruction of the unknown potential with compact support in the 3-d Schr\"odinger equation is considered. Only the modulus of the scattering complex valued wave field is known, whereas the phase is…
The inverse problem of recovery of a potential on a quantum tree graph from Weyl's matrix given at a number of points is considered. A method for its numerical solution is proposed. The overall approach is based on the leaf peeling method…
Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schr\"odinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are…
We present a continuous variable tomography scheme that reconstructs the Husimi Q-function (Wigner function) by Lagrange interpolation, using measurements of the Q-function (Wigner function) at the Padua points, the optimal sampling points…
We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced…
Quantum states are successfully reconstructed using the maximum likelihood estimation on the subspace where the measured projectors reproduce the identity operator. Reconstruction corresponds to normalization of incompatible observations.…
In the present paper, we consider a non self adjoint hyperbolic operator with a vector field and an electric potential that depend not only on the space variable but also on the time variable. More precisely, we attempt to stably and…
Metric reconstruction is the general problem of parameterizing GR in terms of its two ``true degrees of freedom'', e.g., by a complex scalar ``potential'' -- in practice mostly with the aim of simplifying the Einstein equation (EE) within…
Numerical approximation of quantum states via convex combinations of states with positive partial transposes (bi-PPT state) in multipartite systems constitutes a fundamental challenge in quantum information science. We reformulate this…
Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices.…
We review the problem of state reconstruction in classical and in quantum physics, which is rarely considered at the textbook level. We review a method for retrieving a classical state in phase space, similar to that used in medical imaging…