Geodesic
About one method of numerical solution Schrodinger equation
Matematičeskoe modelirovanie, Tome 31 (2019) no. 8, pp. 61-78.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper considers the method of numerical solution of the Schrodinger equation, which, in part, can 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 linear one-dimensional oscillator, hydrogen atom and benzene.
Keywords: Schrodinger equation, numerical methods, Monte-Carlo method. 
@article{MM_2019_31_8_a3,
     author = {K. E. Plokhotnikov},
     title = {About one method of numerical solution {Schrodinger} equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {61--78},
     publisher = {mathdoc},
     volume = {31},
     number = {8},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2019_31_8_a3/}
}
TY  - JOUR
AU  - K. E. Plokhotnikov
TI  - About one method of numerical solution Schrodinger equation
JO  - Matematičeskoe modelirovanie
PY  - 2019
SP  - 61
EP  - 78
VL  - 31
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2019_31_8_a3/
LA  - ru
ID  - MM_2019_31_8_a3
ER  - 
%0 Journal Article
%A K. E. Plokhotnikov
%T About one method of numerical solution Schrodinger equation
%J Matematičeskoe modelirovanie
%D 2019
%P 61-78
%V 31
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2019_31_8_a3/
%G ru
%F MM_2019_31_8_a3
K. E. Plokhotnikov. About one method of numerical solution Schrodinger equation. Matematičeskoe modelirovanie, Tome 31 (2019) no. 8, pp. 61-78. http://geodesic.mathdoc.fr/item/MM_2019_31_8_a3/

[1] Iu.I. Ozhigov, Konstruktivnaia fizika, NITS “Regiuliarnaia i khaoticheskaia dinamika”, M.–Izhevsk, 2010, 424 pp.

[2] N.F. Stepanov, Kvantovaia mekhanika i kvantovaia khimiia, Mir, M., 2001, 519 pp.

[3] Jeongnim Kim, Andrew T. Baczewski, Todd D. Beaudet, et al., “QMCPACK: An open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids”, Journal of Physics Condensed Matter, 30:19 (2018) | DOI

[4] D.R. Hartree, The Calculation of Atomic Structures, Wiley Sons, New York, 1957 | MR | Zbl

[5] W. Kohn, “Nobel Lecture: Electronic structure of matter - wave functions and density functionals”, Reviews of Modern Physics, 71:5, October (1999), 1253–1266 | DOI

[6] L.D. Landau. E.M. Livshits, Quantum Mechanics. Non-relativistic Theory, v. 3, Pergamon Press, Oxford, 1962, 618 pp. | MR

[7] N.S. Akhmetov, Obshchaia i neorganicheskaia khimiia, Vysshaya shkola, Izd. tsentr “Akademiia”, M., 2001, 743 pp.

[8] L. Poling, The Nature of the Chemical Bond, Cornell Univ. Press, Ithaca, N.Y., 1960, 655 pp.

[9] D. Bohm, Quantum Theory, Prentice-Hall, Inc, N.Y., 1951, 672 pp.

[10] V.V. Vedeniapin, T.S. Kazakova, V.Ia. Kiselevskaia-Babinina, B.N. Chetverushkin, “Schrodinger Equation as a Self-Consistent Field”, Doklady Mathematics, 97:3, May (2018), 240–242 | DOI | MR | Zbl