Related papers: Comment on "New analytic solution of Schr\"odinger…

The goal of this paper is to provide an analysis of the ``toolkit'' method used in the numerical approximation of the time-dependent Schr\"odinger equation. The ``toolkit'' method is based on precomputation of elementary propagators and was…

We describe the exact WKB method from the point of view of abelianization, both for Schr\"odinger operators and for their higher-order analogues (opers). The main new example which we consider is the "$T_3$ equation," an order $3$ equation…

This article is aimed at presenting the Schr\"odinger problem and some of its connections with optimal transport. We hope that it can be used as a basic user's guide to Schr\"odinger problem. We also give a survey of the related literature.…

We discuss various relations between part of the results in arXiv:2103.05803v4 and recent author's results.

The aim of this note is to extend recent results of Yajima-Zhang \cite{Y-Z1, Y-Z2} on the 1/2- smoothing effect for Schr\"odinger equation with potential growing at infinity faster than quadratically.

The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This method has already been successfully applied to the case of central potentials of…

We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the…

This is a reply to the comment by M. Kastner and M. Promberger [cond-mat/0011516] on the paper published in J. Stat. Phys. 99, 691 (2000) and also in cond-mat/0002176. We show that all their criticisms do not apply.

In the authors' previous works, novel finite element formulations for the contact interaction of slender beams have been proposed. In their recent article "Consistent Development of a Beam-To-Beam Contact Algorithm via the Curve to Solid…

We consider the existence and multiplicity of solutions for a class of quasi-linear Schr\"{o}dinger equations which include the modified nonlinear Schr\"{o}dinger equations. A new perturbation approach is used to treat the sub-cubic…

A new integrable system of two symmetrically coupled derivative nonlinear Schroedinger equations is detected by means of the singularity analysis. A nonlinear transformation is proposed which uncouples the equations of the new system.

Erroneous statements on the mathematical and physical properties of the double-Kerr solution made in a recent paper (Class. Quantum Grav. 21 (2004) 2723) are commented.

This is a comment on the recent paper by O.V. Selyugin, J.-R. Cudell, and E. Predazzi "Analytic properties of different unitarization schemes" arXiv: 0712.0621v2, [hep-ph]

We systematically describe and classify 1-dimensional Schr\"odinger equations that can be solved in terms of hypergeometric type functions. Beside the well-known families, we explicitly describe 2 new classes of exactly solvable…

We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical…

New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.

The goal of this paper is to provide an analysis of the "toolkit" method used in the numerical approximation of the time-dependent Schr\"odinger equation. The "toolkit" method is based on precomputation of elementary propagators and was…

Time-like orbits in Schwarzschild space-time are presented and classified in a very transparent and straightforward way into four types. The analytical solutions to orbit, time, and proper time equations are given for all orbit types in the…

The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812.2968

It is shown that by means of the approach based on the Quantum Hamilton-Jacobi equation, it is possible to modify the WKB expressions for the energy levels of quantum systems, when incorrect, obtaining exact WKB-like formulae. This extends…