1. Joint Institute for Nuclear Research, Dubna, Moscow Region, 141980, Russia 2. Institute of Mathematics and Informatics, BAS, Sofia, Bulgaria 3. Future University-Hakodate, Hakodate, 041-8655, Japan
Abstract:
The operator-difference multi-layer (ODML) schemes for solving the time-dependent Schrödinger equation (TDSE) till six order accuracy by a time step are presented. The reduced schemes for solving a set of the coupled TDSE’s are devised by using a set of appropriate basis angular functions and a finite element method with respect to a hyper-radial variable. Convergence by a number of the basis functions and efficiency of the numerical schemes are demonstrated in the case of an exactly solvable model of the two-dimensional oscillator in time-depended electric fields.