Discrete variable representation method calculation of the electronic structure of noble gas atoms

We have been calculated the ground state charge densities and energies of noble gas atoms through a single time dependent quantum fluid Schr$\ddot{o}$dinger equation. By using imaginary - time, the Schr$\ddot{o}$dinger equation has been transformed into diffusion equation. This equation numerically solved through discrete variable representation (DVR) method. Instead of the usual finite difference method the radial coordinate is discretized using the discrete variable representation constructed from Coulomb wave functions. Our calculations were performed using the Mathematica 7.0 programm.