Geodesic
On the statistical generator of solutions to the Schrodinger equation
Matematičeskoe modelirovanie, Tome 34 (2022) no. 12, pp. 75-90

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The article describes the procedure for generating solutions to the Schrödinger equation by the Monte Carlo method. As a demonstration quantum system illustrating this generator, clusters of water: hexamer 6(H$_2$O), dodecamer 12(H$_2$O) and tetradecamer 14(H$_2$O) act. The generator of solutions to the Schrödinger equations is derived from the algorithm proposed by the author earlier, based on the intersection of the finite-difference and Monte Carlo approaches, as well as methods of spatial reduction of scattering centers of particle nuclei and scattering centers of electrons of an arbitrary quantum system, tested on water clusters. As a result of this information, it turned out to be possible to construct an algorithm for generating an unlimited number of different spatial structures of scattering clouds of particle nuclei and electrons at the same dissociation energy of a quantum system.
Keywords: Schrodinger equation solution generator, numerical methods, ordinary differential equations, Monte Carlo method, average positions of quantum system particles, water cluster. 
@article{MM_2022_34_12_a4,
     author = {K. E. Plokhotnikov},
     title = {On the statistical generator of solutions to the {Schrodinger} equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {75--90},
     publisher = {mathdoc},
     volume = {34},
     number = {12},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2022_34_12_a4/}
}
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K. E. Plokhotnikov. On the statistical generator of solutions to the Schrodinger equation. Matematičeskoe modelirovanie, Tome 34 (2022) no. 12, pp. 75-90. http://geodesic.mathdoc.fr/item/MM_2022_34_12_a4/