A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular exam...

With the use of a variant of the method of separation of variables, the initial value problem for the time-dependent linear Schrödinger equation is solved exactly for a large class of potential functions related to multisoliton interactions in the vector nonlinear Schrödinger equation. Completeness of states is proved for absolutely continuous initial data in L1. Copyright © 1998 Elsevier Scien...

A class of stochastic particle models for the spatially discretized time-dependent Schrödinger equation is constructed. Each particle is characterized by a complex-valued weight and a position. The particle weights change according to some deterministic rules between the jumps. The jumps are determined by the creation of offspring. The main result is that certain functionals of the particle sys...

We present a numerical study of a derivative nonlinear Schrödinger equation with a general power nonlinearity, |ψ| ψx. In the L-supercritical regime, σ > 1, our simulations indicate that there is a finite time singularity. We obtain a precise description of the local structure of the solution in terms of blowup rate and asymptotic profile, in a form similar to that of the nonlinear Schrödinger ...

In this paper, we first established a high-accuracy difference scheme for the time-fractional Schrödinger equation (TFSE), where factional term is described in Caputo derivative. We used L1-2-3 formula to approximate derivative, and fourth-order compact finite utilized discretizing spatial term. The unconditional stability convergence of maximum norm are proved. Finally, verified theoretical re...

Comparison of Finite Differences and WKB Method for Approximating Tunneling Times of the One Dimensional Schrödinger Equation Student: Yael Elmatad Overview The goal of this research was to examine the quantum mechanical phenomenon of tunneling with respect to the Schrödinger Equation. A quantum mechanical wave is said to “tunnel” when it travels (propagates) through a classically forbidden reg...