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Regularization of Coulomb potential for calculating electron density in quantum mechanical systems

Kshevetskty S., Shapilov A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2017

Vol. 21, No 2

177--184

In this paper we show a simple and effective method for regularizing the Coulomb potential for numerical calculations of quantum mechanical problems, such as, for example, the solution of the Schrödinger equation, the expansion of charge density and others. The introduction explains why the regularization of the Coulomb potential is important. In the second part, the regularization method itself as well as its advantages and disadvantages will be described in detail. The third part demonstrates some numerical calculations for the Sulfur + Hydrogen system using the proposed method. In the final part, the obtained results are summed up.

A Note on Scattering in Deformed Space with Minimal Lenght

Stetsko M. M.

Computational Methods in Science and Technology

2010

Vol. 16, No. 2

195-199

We consider the elastic scattering in deformed space with minimal length. We give the basic relation for the elastic scattering in deformed space. We also investigate the partial wave method in deformed space. It is shown that the relations for the scattering amplitude and cross-section formally coincides with ordinary ones.

Efficient computation of the MCTDHF approximation to the time-dependent Schrodinger equation

Koch O.

Opuscula Mathematica

2006

Vol. 26, no. 3

483-497

We discuss analytical and numerical properties of the multi-configuration time-dependent Hartree-Fock method for the approximate solution of the time-dependent multi-particle (electronic) Schrödinger equation which are relevant for an efficient implementation of this model reduction technique. Particularly, we focus on a discretization and Iow rank approximation in the evaluation of the meanfield terms occurring in the MCTDHF equations of motion, which is crucial for the computational tractability of the problem. We give error bounds for this approximation and demonstrate the achieved gain in performance.