The paper presents a parallelisation scheme for solving the non-stationary three-dimensional Schrödinger equation. The problem is studied in the DVR (Discrete Variable Representation) framework, where the original equation is reduced to a system of ordinary differential equations (ODEs). A component-wise splitting method is used for numerical integration, enabling efficient computation by dividing the problem into independent subproblems. The study demonstrates that key computational steps, such as vector transformations and matrix diagonalisation, can be effectively parallelised. Numerical simulation results are provided, showcasing a significant reduction in computation time for problems requiring a large number of grid points in temporal and spatial variables.