Related papers: On uniqueness and nonuniqueness for potential reco…

We investigate the increasing stability of the inverse Schr\"{o}dinger potential problem with integer power type nonlinearities at a large wavenumber. By considering the first order linearized system with respect to the unknown potential…

Renormalizability of the (minimal) single-fermion QED extension is investigated at all orders of perturbation theory in the framework of algebraic renormalization, a regularization-independent method. Relative to the standard QED, new…

The uniqueness of the positive ground state solutions of fractional Shrodinger equations with a harmonic potential has not been covered by the breakthrough method developed in [1, 2]. It has remained an open question for years. [3] and [5]…

This article addresses the inverse problem of simultaneously recovering both the wave speed coefficient and an unknown initial condition (acting as the source) for the multidimensional wave equation from a single passive boundary…

In this work, we will prove a uniqueness result for Calder\'on's inverse problem via some integral representation formulas for solutions of the Vekua equation in the framework of Clifford analysis.

Within the framework of the individuality interpretation of quantum theory (QT), the basic equations of QT cannot be derived from the basic equations of classical mechanics (CM). The unbridgeable gap between CM and QT is given by the fact…

In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that,…

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…

We consider Sturm-Liouville operators on geometrical graphs without cycles (trees) with singular potentials from the class $W_2^{-1}$. We suppose that the potentials are known on a part of the graph, and study the so-called partial inverse…

This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…

This paper investigates the nonlinear Schr\"{o}dinger equation with a singular convolution potential. It demonstrates the local well-posedness of this equation in a modified Sobolev space linked to the energy. Additionally, we derive…

In this work we study the phenomenon of increasing stability in the inverse boundary value problem for the Schr\"odinger equation. This problem was previously considered by Isakov in which he discussed the phenomenon in different ranges of…

The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…

We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…

In this article we have developed a formalism to obtain the Schr$\ddot{\rm{o}}$dinger equation for a particle in a frame undergoing an uniform acceleration in an otherwise flat Minkowski space-time geometry. We have presented an exact…

Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov…

This paper tackles the data completion problem related to the Helmholtz equation. The goal is to identify unknown boundary conditions on parts of the boundary that cannot be accessed directly, by making use of measurements collected from…

Quantum anomalies in the inverse square potential are well known and widely investigated. Most prominent is the unbounded increase in oscillations of the particle's state as it approaches the origin when the attractive coupling parameter is…

We prove uniqueness and stability for the inverse boundary value problem of the two dimensional Schr\"odinger equation. We do not assume the potentials to be continuous or even bounded. Instead, we assume that some of their positive…

We consider increasing stability in the inverse Schr\"{o}dinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are…