Related papers: An Evolutionary approach for solving Shr\"odinger …

Using a variational approach based on a Lagrangian formulation and Gaussian trial functions, we derive a simple dynamical system that captures the main features of the time-dependent Schr\"odinger-Newton equations. With little analytical or…

In this paper, we present a machine learning method for the discovery of analytic solutions to differential equations. The method utilizes an inherently interpretable algorithm, genetic programming based symbolic regression. Unlike…

We here show how the methods recently applied by [DW16] to solve the stochastic nonlinear Schr\"odinger equation on $\mathbb{T}^2$ can be enhanced to yield solutions on $\mathbb{R}^2$ if the non-linearity is weak enough. We prove that the…

The time dependent complex Schr\"odinger equation with cubic nonlinearity is solved by constructing differential quadrature algorithm based on sinc functions. Reduction to a coupled system of real equations enables to approach the space…

For almost 75 years, the general solution for the Schr\"odinger equation was assumed to be generated by an exponential or a time-ordered exponential known as the Dyson series. We study the unitarity of a solution in the case of a singular…

We show that a rectangular collocation method, equivalent to evaluating all matrix elements with a quadrature-like scheme and using more points than basis functions, is an effective approach for solving the electronic Schr\"odinger equation…

We propose a new approach for the solution of initial value problems for integrable evolution equations in the periodic setting based on the unified transform. Using the nonlinear Schr\"odinger equation as a model example, we show that the…

The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary…

A novel method is proposed to determine an analytical expression for eigenfunctions and numerical result for eigenvalues of the Schr\"odinger type equations, within the context of Taylor expansion of a function. Optimal truncation of the…

For small number of equations, systems of linear (and sometimes nonlinear) equations can be solved by simple classical techniques. However, for large number of systems of linear (or nonlinear) equations, solutions using classical method…

In this paper, we propose a quantum algorithm that combines the momentum accelerated gradient method with Schr\"odingerization [S. Jin, N. Liu and Y. Yu, Phys. Rev. Lett, 133 (2024), 230602][S. Jin, N. Liu and Y. Yu, Phys. Rev. A, 108…

In this letter we present an analytic evidence of the non-integrability of the discrete nonlinear Schroedinger equation, a well-known discrete evolution equation which has been obtained in various contexts of physics and biology. We use a…

We show how the Laplace transform can be used to give a solution of the time-dependent Schr\"odinger equation for an arbitrary initial wave packet if the solution of the stationary equation is known. The solution is obtained without summing…

S-state Bound state solution to Schroedinger equation for an exponential potential is derived using the Mellin transform. This method is a new and an alternative to the usual method of reducing Schroedinegr equation to a Bessel differential…

We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schr\"odinger equations. The accuracy and computing speed can be systematically and arbitrarily increased to orders of…

The use of Evolutionary Algorithms (EA) for solving Mathematical/Computational Optimization Problems is inspired by the biological processes of Evolution. Few of the primitives involved in the Evolutionary process/paradigm are selection of…

This paper introduces weighted finite difference methods for numerically solving dispersive evolution equations with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled cubic nonlinear…

We present a quantum computational framework that systematically converts classical linear iterative algorithms with fixed iteration operators into their quantum counterparts using the Schr\"odingerization technique [Shi Jin, Nana Liu and…

We develop a quantum algorithm for solving high-dimensional time-fractional heat equations. By applying the dimension extension technique from [FKW23], the $d+1$-dimensional time-fractional equation is reformulated as a local partial…

We present a novel approach for solving the time-dependent Schr\"{o}dinger equation (TDSE). The method we propose converts the TDSE to an equivalent Volterra integral equation; introducing a global Lagrange interpolation of the integrand…