Multi-Layer Schemes for Solving the Time-Dependent Shr.odinger Equation

The algorithm based on unitary evolution operator decomposition to generate in a
MAPLE and REDUCE packages multi-layer implicit schemes for numerical solving the
time-dependent Shroedinger equation is presented. The optimal methods for construction
of additional gauge transformations to extract symmetric operators needed for generation
economical algebraic evolution schemes with respect to spatial variables by the finite element
method are studied. The efficiency of the developed computational schemes till sixth
order with respect to the time step and till seven order with respect to the spatial step, are
demonstrated on the integrable model of oscillator in a time-dependent external field.

нестационарное уравнение Шрёдингера, задача Коши, разложение оператора эволюции, калибровочные преобразования, операторно-разностные многослойные схемы, метод конечных элементов