In this paper, we study the simulation of nonlinear Schrödinger equation in one, two and three dimensions. The proposed method is based on a time-splitting method that decomposes the original problem into two parts, a linear equation and a nonlinear equation. The linear equation in one dimension is approximatedwith the Chebyshev pseudo-spectral collocationmethod in space variable and the Crank–...

The discretized Schrödinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schrödinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unf...

The discretized Schrödinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schrödinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unf...

in order to represent the potential energy function over the whole range of r, many potentialenergy functions have been proposed. in the present paper, we employ many potential energyfunctions, to use numerov method for solving the nuclear schrödinger equation for the ifmolecule, as an example of a heteronuclear diatomic molecules. then we determine thespectroscopic constants eω , e e x ω , e b...

We prove the theorem announced in Phys. Rev. Lett. 85:5022, 2001 concerning the existence and properties of fractal states for the Schrödinger equation in the infinite one-dimensional well.