Related papers: Reference potential approach to the quantum-mechan…
In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A…
Inversion of the K-fold stochastic autoconvolution integral equation is an elementary nonlinear problem, yet there are no de facto methods to solve it with finite statistics. To fix this problem, we introduce a novel inverse algorithm based…
This is the fourth article in a series where we succeed in enlarging the class of exactly solvable quantum systems. We do that by working in a complete set of square integrable basis that carries a tridiagonal matrix representation for the…
The "Krein" regularization method of quantum field theory is studied, inspired by the Krein space quantization and quantum metric fluctuations. It was previously considered in the one-loop approximation, and this paper is generalized to all…
The direct and inverse scattering problems on the full line are analyzed for a first-order system of ordinary linear differential equations associated with the derivative nonlinear Schr\"odinger equation and related equations. The system…
Central idea: To obtain the interaction potential using the inverse scattering method, we have employed the Physics-Informed Machine Learning (PIML) approach. In this framework, the machine learning algorithm is guided by the underlying…
In this work, a complete solution of the inverse spectral problem for a class of Dirac differential equations system is given by spectral data (eigenvalues and normalizing numbers). As a direct problem, the eigenvalue problem is solved: the…
Asymptotic iteration method (AIM) is used to find the exact analytical solutions of the one dimensional Klein-Gordon equation for the q-deformed Manning-Rosen potential with equal Lorentz vector and scalar potential. The bound state…
Two-body interactions of elementary particles are useful in particle and nuclear physics to describe qualitatively and quantitatively few- and many-body systems. We are extending for this purpose the quantum inversion approach for systems…
Determining kinetic rate constants is a highly relevant problem in biochemistry, so various methods have been designed to extract them from experimental data. Such methods have two main components: the experimental apparatus and the…
We use inverse scattering methods, generalized for a specific class of complex potentials, to construct a one parameter family of complex potentials V(s, r) which have the property that the zero energy s-wave Jost function, as a function of…
A method, recently devised to obtain analytical approximations to certain classes of integrals, is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of…
In this work we demonstrate how different semi-classical methods can be combined in a novel way to reconstruct the perturbation potential of ultra compact stars. Besides rather general assumptions, the only specific information entering…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…
The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit…
This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…
In this paper we show how the quantum mechanics of the inverted harmonic oscillator can be mapped to the quantum mechanics of a particle in a super-critical inverse square potential. We demonstrate this by relating both of these systems to…
We reexamine and extend a group of solutions in series of Bessel functions for a limiting case of the confluent Heun equation and, then, apply such solutions to the one-dimensional Schr\"odinger equation with an inverted quasi-exactly…