# Absorbing boundary conditions for the time-dependent Schrödinger-type equations in R3

@article{Wu2019AbsorbingBC, title={Absorbing boundary conditions for the time-dependent Schr{\"o}dinger-type equations in R3}, author={Xiaojie Wu and Xiaotao Li}, journal={Physical review. E}, year={2019}, volume={101 1-1}, pages={ 013304 } }

Absorbing boundary conditions are presented for three-dimensional time-dependent Schrödinger-type of equations as a means to reduce the cost of the quantum-mechanical calculations. The boundary condition is first derived from a semidiscrete approximation of the Schrödinger equation with the advantage that the resulting formulas are automatically compatible with the finite-difference scheme and no further discretization is needed in space. The absorbing boundary condition is expressed as a…

## One Citation

### A Machine-Learning Method for Time-Dependent Wave Equations over Unbounded Domains

- Computer Science, MathematicsArXiv
- 2021

A machine-learning method to solve time-dependent wave equations using a neural network, trained using wave packets that are parameterized by their band width and wave numbers, which provides an interesting alternative for finite-time simulation of wave propagation.

## References

SHOWING 1-10 OF 79 REFERENCES

### Integral boundary conditions for the time-dependent Schrödinger equation: Atom in a laser field

- Physics
- 1999

We formulate exact integral boundary conditions for a solution of the time-dependent Schrodinger equation that describes an atom interacting, in the dipole approximation, with a laser pulse. These…

### Weak Ill-Posedness of Spatial Discretizations of Absorbing Boundary Conditions for Schrödinger-Type Equations

- Mathematics
- 2002

When we wish to solve numerically a differential problem defined on an infinite domain, it is necessary to consider a finite subdomain and to use artificial boundary conditions in such a way that the…

### Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability

- Mathematics, Computer Science
- 2003

Stability of the resulting initialboundary value scheme is proved, error estimates for the considered approximation of the boundary condition are given, and the efficiency of the proposed method is illustrated on several examples.

### Absorbing Boundary Conditions for the Schrödinger Equation

- MathematicsSIAM J. Sci. Comput.
- 1999

General absorbing boundary conditions will be developed for the Schrodinger equation with one spatial dimension, using group velocity considerations, and previously published absorbing boundary Conditions will be shown to reduce to special cases of this absorbing boundary condition.

### Adaptive absorbing boundary conditions for Schrödinger-type equations: Application to nonlinear and multi-dimensional problems

- MathematicsJ. Comput. Phys.
- 2007

### Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation

- Mathematics
- 2003

### Absorbing boundary conditions for time-dependent Schrödinger equations: A density-matrix formulation.

- MathematicsThe Journal of chemical physics
- 2019

The boundary conditions are expressed in terms of the elements of the density-matrix, and it is derived from the full model over a much larger domain, and several approximations for the convolution integral will be constructed with guaranteed stability.

### Exact artificial boundary conditions for the Schrödinger equation in $R ^2$

- Mathematics
- 2004

In this paper, we propose a class of exact artificial boundary conditions for the numerical solution of the Schrodinger equation on unbounded domains in two-dimensional cases. After we introduce a…

### EXACT ARTIFICIAL BOUNDARY CONDITIONS FOR SCHRÖDINGER EQUATION IN R2∗

- Mathematics
- 2004

In this paper, we propose a class of exact artificial boundary conditions for the numerical solution of the Schrödinger equation on unbounded domains in two-dimensional cases. After we introduce a…

### Efficient representation of nonreflecting boundary conditions for the time‐dependent Schrödinger equation in two dimensions

- Mathematics
- 2008

We present a fast algorithm for the evaluation of exact, nonreflecting boundary conditions for the time‐dependent Schrödinger equation in two dimensions on the unit circle. After separation of…