Numerical Solution of the Time Dependent 3D Schrödinger Equation Describing Tunneling of Atoms from Anharmonic Traps

We present an efficient numerical method for the integration of the 3D Schrödinger equation. A tunneling problem of two interacting bosonic atoms confined in a 1D anharmonic trap has been successfully solved by means of this method. We demonstrate fast convergence of the final results with respect to spatial and temporal grid steps. The computational scheme is based on the operator-splitting technique with the implicit Crank-Nicolson algorithm on spatial sixth-order finite-differences. The computational time is proportional to the number of spatial grid points.