A high-order accuracy method for numerical solving of the time-dependent Schrödinger equation
The paper presents the implicit difference \(O(\tau^{2m})\)-schemes in terms of the Magnus expansion for the evolution operator of the time-dependent Schrödinger equation and its further factorization with the help of diagonal Padé approximations. These schemes can be viewed as generalization of the well-known Crank-Nicolson algorithm. The efficiency of the method is illustrated by numerical experiments for the oscillator with time-dependent frequency.
scientific article; zbMATH DE number 1394619