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.