In this paper, we construct discrete artificial boundary conditions to solve the one-dimensional time-dependent Schrodinger equation on unbounded domain. After introducing an artificial boundary, we get an initial-boundary value problem with a finite computational domain which is equivalent to the original problem. Then we propose a polynomial basis set that is extendable to any desired higher-order accuracy. This method is based on the Constrained Interpolation Profile(CIP) method and it's a kind of semi-Lagrangian scheme . In this study, CIP method is applied and analytical results with the finite difference method compared. The results obtained in this study have clarified that the CIP method provides higher accuracy than those obtained using the finite difference method.
moeini, M. & ghorbani, M. (2026). Discrete Artificial Boundary Conditions for the Time-Dependent Schrodinger Equation. (e743120). Mathematics and Computational Sciences, (), e743120 https://doi.org/10.30511/mcs.2026.2087501.1776
MLA
moeini, M., & ghorbani, M. "Discrete Artificial Boundary Conditions for the Time-Dependent Schrodinger Equation" .e743120 , Mathematics and Computational Sciences, , 2026, e743120. doi: 10.30511/mcs.2026.2087501.1776
HARVARD
moeini, M., & ghorbani, M. (2026). 'Discrete Artificial Boundary Conditions for the Time-Dependent Schrodinger Equation', Mathematics and Computational Sciences, (), e743120. doi: 10.30511/mcs.2026.2087501.1776
CHICAGO
moeini, M. & ghorbani, M., "Discrete Artificial Boundary Conditions for the Time-Dependent Schrodinger Equation." Mathematics and Computational Sciences, (2026): e743120, doi: 10.30511/mcs.2026.2087501.1776
VANCOUVER
moeini M., ghorbani M. Discrete Artificial Boundary Conditions for the Time-Dependent Schrodinger Equation. MCS. 2026;():e743120. doi: 10.30511/mcs.2026.2087501.1776
