Efficient algorithm for TD-Schrödinger equation and TD-Kohn–Sham equation Original Research Article

A computational method for solving the time-evolution of wave functions which obey the time-dependent Schrödinger or Kohn–Sham equation has been developed. Due to the time-dependence of the effective Hamiltonian in the TD-Kohn–Sham equation, the numerical schemes have not been clear so far. In this work, we develop a different approach for studying the formal solution of the TD-Kohn–Sham equation, and find that it can efficiently and accurately be solved by using the split operator technique.