Geodesic
Numerical method for reconstructing the average positions of quantum particles in a molecular system
Matematičeskoe modelirovanie, Tome 32 (2020) no. 9, pp. 20-34

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The article develops a numerical method for solving the Schrodinger equation, proposed in the author's previous work. In the method described earlier, there was uncertainty in identifying the average positions of quantum particles in the molecular system; they were set for external reasons without considering the Schrodinger equation itself. In this paper, a list of procedures for numerical identification of the average positions (scattering centers) of particles of an arbitrary molecular system is formulated for the subsequent application of the Monte Carlo algorithm for solving the corresponding Schrodinger equation. Several examples of application of the proposed numerical procedures for calculating such molecular systems as atom, hydrogen molecule, water, benzene (in several modifications), as well as hypothetical multihydrogen are considered.
Keywords: Schrodinger equation, numerical methods, ordinary differential equations and Monte-Carlo method. 
@article{MM_2020_32_9_a1,
     author = {K. E. Plokhotnikov},
     title = {Numerical method for reconstructing the average positions of quantum particles in a molecular system},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {20--34},
     publisher = {mathdoc},
     volume = {32},
     number = {9},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_9_a1/}
}
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K. E. Plokhotnikov. Numerical method for reconstructing the average positions of quantum particles in a molecular system. Matematičeskoe modelirovanie, Tome 32 (2020) no. 9, pp. 20-34. http://geodesic.mathdoc.fr/item/MM_2020_32_9_a1/