# A short note on simplified pseudospectral methods for computing ground state and dynamics of spherically symmetric Schrödinger-Poisson-Slater system

@article{Dong2011ASN, title={A short note on simplified pseudospectral methods for computing ground state and dynamics of spherically symmetric Schr{\"o}dinger-Poisson-Slater system}, author={Xuanchun Dong}, journal={J. Comput. Phys.}, year={2011}, volume={230}, pages={7917-7922} }

## 8 Citations

### Exact Artificial Boundary Condition for the Poisson Equation in the Simulation of the 2D Schrödinger-Poisson System

- Mathematics
- 2014

We study the computation of ground states and time dependent solutions of the Schrodinger-Poisson system (SPS) on a bounded domain in 2D (i.e. in two space dimensions). For a disc-shaped domain and…

### Dimension Reduction of the Schrödinger Equation with Coulomb and Anisotropic Confining Potentials

- PhysicsSIAM J. Appl. Math.
- 2013

Efficient and accurate numerical methods for computing ground states and dynamics of the SAM, SDM, and LAM models are presented and applied to find numerically convergence and convergence rates for the dimension reduction from 3D to 2D and3D to 1D in terms of ground state and dynamics.

### A splitting Chebyshev collocation method for Schrödinger–Poisson system

- Mathematics
- 2018

We develop a splitting Chebyshev collocation (SCC) method for the time-dependent Schrödinger–Poisson (SP) system arising from theoretical analysis of quantum plasmas. By means of splitting technique…

### Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT

- Computer ScienceJ. Comput. Phys.
- 2015

### SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations

- MathematicsElectronic Research Archive
- 2022

In this paper, a fully discrete scheme is proposed to solve the nonlinear Schrödinger-Possion equations. The scheme is developed by the scalar auxiliary variable (SAV) approach, the Crank-Nicolson…

### One-dimensional fuzzy dark matter models: Structure growth and asymptotic dynamics

- Physics
- 2021

This paper investigates the feasibility of simulating Fuzzy Dark Matter (FDM) with a reduced number of spatial dimensions. Our aim is to set up a realistic, yet numerically inexpensive, toy model in…

### A splitting Chebyshev collocation method for Schrödinger–Poisson system

- MathematicsComputational and Applied Mathematics
- 2018

We develop a splitting Chebyshev collocation (SCC) method for the time-dependent Schrödinger–Poisson (SP) system arising from theoretical analysis of quantum plasmas. By means of splitting technique…

### Optimal Error Estimates of Compact Finite Difference Discretizations for the Schrodinger-Poisson System

- Mathematics
- 2013

We study compact finite difference methods for the Schrodinger-Poisson equation in a bounded domain and establish their optimal error estimates under proper regularity assumptions on wave function…

## References

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We study a mixed-state Schrodinger–Poisson–Slater system (SPSS). This system combines the nonlinear and nonlocal Coulomb interaction with a local potential nonlinearity known as the "Slater exchange…

### Long-Time Dynamics of the Schrödinger–Poisson–Slater System

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In this paper we analyze the asymptotic behaviour of solutions to the Schrödinger–Poisson–Slater (SPS) system in the frame of semiconductor modeling. Depending on the potential energy and on the…

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Abstract. A Schrödinger-Poisson model describing the stationary behavior of a quantum device away from equilibrium is proposed and analyzed. In this model, current carrying scattering states of the…

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The Schrödinger-Poisson-Xα (S-P-Xα) model is a “local one particle approximation” of the time dependent Hartree-Fock equations. It describes the time evolution of electrons in a quantum model…

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We prove the existence and uniqueness of stationary spherically symmetric positive solutions for the Schr\"{o}dinger-Newton model in any space dimension $d$. Our result is based on an analysis of the…

### Local Existence and WKB Approximation of Solutions to Schrödinger–Poisson System in the Two-Dimensional Whole Space

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We consider the Schrödinger–Poisson system in the two-dimensional whole space. A new formula of solutions to the Poisson equation is used. Although the potential term solving the Poisson equation may…

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This work considers the Cauchy problem of the two-dimensional Schrodinger–Poisson system in the energy class and decomposes the nonlinearity into a sum of the linear logarithmic potential and a good remainder, which enables the perturbation method to apply.

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A novel fast Spectral Element Method (SEM) with spectral accuracy for the self-consistent solution of the Schrödinger-Poisson system has been developed for the simulation of semiconductor…