Abstract
The paper considers the method of the numerical solution of the Schrodinger equation, which can partly be attributed to the class of Monte Carlo methods. The method is presented and simultaneously illustrated by the examples of solving the one-dimensional and multidimensional Schrodinger equation in the problems of a linear one-dimensional oscillator, hydrogen atom, and benzene atom.
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REFERENCES
Yu. I. Ozhigov, Constructive Physics (Regular. Khaotich. Dinamika, Moscow, Izhevsk, 2010) [in Russian].
N. F. Stepanov, Quantum Mechanics and Quantum Chemistry (Mir, Moscow, 2001).
J. Kim, A. T. Baczewski, T. D. Beaudet, et al., “QMCPACK: an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids,” J. Phys.: Condens. Matter 30 (19) (2018). https://doi.org/10.1088/1361-648X/aab9c3
D. R. Hartree, The Calculation of Atomic Structures (Wiley, New York, 1957).
W. Kohn, “Nobel Lecture: Electronic structure of matter - wave functions and density functionals,” Rev. Mod. Phys. 71, 1253–1266 (1999).
L. D. Landau and E. M. Livshits, Course of Theoretical Physics, Vol. 3: Quantum Mechanics. Non-Relativistic Theory (Nauka, Moscow, 1974; Pergamon, Oxford, 1962).
N. S. Akhmetov, General and Inorganic Chemistry (Vysshaya Shkola, Akademiya, Moscow, 2001) [in RUssian].
L. Poling, The Nature of the Chemical Bond (Cornell Univ. Press, Ithaca, New York, 1960).
D. Bohm, Quantum Theory (Prentice-Hall, New York, 1951).
V. V. Vedenyapin, T. S. Kazakova, V. Ya. Kiselevskaia-Babinina, and B. N. Chetverushkin, “Schrödinger equation as a self-consistent field,” Dokl. Math. 97, 240–242 (2018). https://doi.org/10.1134/S1064562418030122
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Plokhotnikov, K.E. About One Method of Numerical Solution of Schrodinger’s Equation. Math Models Comput Simul 12, 221–231 (2020). https://doi.org/10.1134/S2070048220020106
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DOI: https://doi.org/10.1134/S2070048220020106