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Landau, L.D. and Livshits, E.M. (1974) Quantum Mechanics. Non-Relativistic Theory. Vol. 3, Pergamon Press, Moscow, 752 p.

has been cited by the following article:

• TITLE: Solving the Schrodinger Equation on the Basis of Finite-Difference and Monte-Carlo Approaches

  AUTHORS: Konstantin Eduardovich Plokhotnikov

  KEYWORDS: Schrodinger Equation, Numerical Methods, Finite Difference and Monte-Carlo Methods

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.2, February 26, 2021

  ABSTRACT: The paper presents a method of numerical solution of the Schrodinger equation, which combines the finite-difference and Monte-Carlo approaches. The resulting method was effective and economical and, to a certain extent, not improved, i.e. optimal. The method itself is formalized as an algorithm for the numerical solution of the Schrodinger equation for a molecule with an arbitrary number of quantum particles. The method is presented and simultaneously illustrated by examples of solving the one-dimensional and multidimensional Schrodinger equation in such problems: linear one-dimensional oscillator, hydrogen atom, ion and hydrogen molecule, water, benzene and metallic hydrogen.