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The inherently homogeneous stationary-state and time-dependent Schroedinger equations are often recast into inhomogeneous form in order to resolve their solution nonuniqueness. The inhomogeneous term can impose an initial condition or, for…
Schroedinger equation with imaginary PT-symmetric potential $V^{}(x) = i\,x^3$ is studied using the numerical discretization methods in both the coordinate and momentum representations. In the former case our results confirm that the model…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
In studies of quantum squeezing, the emphasis is typically placed more on specific squeezed states and their evolution rather than on the dynamical operations that could simultaneously squeeze a broader range of quantum states, regardless…
The motion of a quantum particle constrained to a two-dimensional non-compact Riemannian manifold with non-trivial metric can be described by a flat-space Schroedinger-type equation at the cost of introducing local mass and metric and…
We present a generic and systematic approach for constructing D-dimensional lattice models with exactly solvable d-dimensional boundary states localized to corners, edges, hinges and surfaces. These solvable models represent a class of…
The quantum marginal problem asks, given a set of reduced quantum states of a multipartite system, whether there exists a joint quantum state consistent with these reduced states. The quantum marginal problem is known to be hard to solve in…
We relax the regularity condition on potentials of Schr\"odinger equations in the uniqueness results in \cite{EB} and \cite{IY2} for the inverse boundary value problem of determining a potential by Dirichlet-to-Neumann map.
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is…
We study a general discrete boundary value problem in Sobolev--Slobodetskii spaces in a plane quadrant and reduce it to a system of integral equations. We show a solvability of the system for a small size of discreteness starting from a…
This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…
We consider the inverse problem of the reconstruction of a Schr\"odinger operator on a unknown Riemannian manifold or a domain of Euclidean space. The data used is a part of the boundary $\Gamma$ and the eigenvalues corresponding to a set…
We investigate nonregular elliptic problems with boundary conditions of higher orders. We prove that these problems are Fredholm on appropriate pairs of inner product H\"ormander spaces that form a two-sided refined Sobolev scale. We also…
A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology…
Numerous lines of experimental, numerical and analytical evidence indicate that it is surprisingly easy to locate optimal controls steering quantum dynamical systems to desired objectives. This has enabled the control of complex quantum…
We establish $L_{q,p}$-estimates and solvability for mixed Dirichlet-conormal problems for parabolic equations in a cylindrical Reifenberg-flat domain with a rough time-dependent separation.
The problem of quantum state preparation is one of the main challenges in achieving the quantum advantage. Furthermore, classically, for multi-level problems, our ability to solve the corresponding quantum optimal control problems is rather…
We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…
We study a model elliptic pseudo-differential equation and simplest boundary value problems for a half-space and a special cone in Sobolev--Slobodetskii spaces which have different smoothness with respect to separate variables. Sufficient…
By converting the rectangular basis potential V(x,y) into the form as V(r)+V(r, phi) described by the pseudo central plus noncentral potential, particular solutions of the two dimensional Schrodinger equation in plane-polar coordinates have…