This thesis focuses on the development and the implementation of domain decomposition methods for the linear and non-linear, one dimensional and two dimensional Schrödinger equations. In the first part, we focus on the Schwarz waveform relaxation method (SWR) for the one dimensional Schrödinger equation. In the case the potential is linear and time-independent, we propose a new algorithm that i...

In order to represent the potential energy function over the whole range of R, many potentialenergy functions have been proposed. In the present paper, we employ many potential energyfunctions, to use Numerov method for solving the nuclear Schrödinger equation for the IFmolecule, as an example of a heteronuclear diatomic molecules. Then we determine thespectroscopic constants eω , e e x ω , e B...

We obtain a time-dependent Schrödinger equation for the Friedmann Robertson Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necesary to include an additional action invariant under the reparametrization of time. The last one does not change the equations of motion of the system, but changes only the constraint which at the quantum level...