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 consider the long time behavior of solutions of the d-dimensional linear Boltzmann equation that arises in the weak coupling limit for the Schrödinger equation with a time-dependent random potential. We show that the intermediate mesoscopic time limit satisfies a Fokker-Planck type equation with the wave vector performing a Brownian motion on the (d − 1)-dimensional sphere of constant energy...

Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schrödinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without assuming that the nuclei are localized to vanishing domains. The derivation, based on a Hamiltonian system interpretation of the Schrödinger equation and stabil...

In this paper, the numerical solution methods of one- particale, one – dimensional time- independentSchrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function V(x). These methods included the FEM(Finite Element Method), Cooly, Numerov and others. Here we considered the Numerov method inmore details...

1 Schrödinger Equation and Time Development Operators 1 1.1 Schrödinger’s equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Time-dependent kets and operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Solutions to Schrödinger’s equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Time developme...