Numerical Solution of the Time Dependent 3D Schrödinger Equation Describing Tunneling of Atoms from Anharmonic Traps
1 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russian Federation
2 Al-Farabi Kazakh National University, Almaty 050040, Republic of Kazakhstan
3 Institute of Nuclear Physics, the Ministry of Energy of the Republic of Kazakhstan, Almaty 050032, Republic of Kazakhstan
4 K.I. Satpaev Institute of Geological Sciences, Almaty 050010, Republic of Kazakhstan
5 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russian Federation
Published online: 14 February 2018
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.
© The Authors, published by EDP Sciences, 2018
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