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.
Highlights
The paper [1] draws attention to the fact that the Schrodinger equations describing the dynamics of most interesting quantum systems cannot be obtained constructively due to the large dimension of the wave function
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
If the quantum system includes n particles, the wave function ψ will depend on 1 + 3n arguments, i.e
Summary
The paper [1] draws attention to the fact that the Schrodinger equations describing the dynamics of most interesting quantum systems cannot be obtained constructively due to the large dimension of the wave function. Monte-Carlo quantum method [3] [4], this problem is solved in different ways. We consider a method for solving the Schrodinger equation, which will allow us to overcome this non-constructivity. In terms of positioning a set of subparticles in a space of dimension 3n, a specially prepared random procedure is used, repeated use of this procedure allows to reconstruct the distribution of the average positions of the quantum particles of a molecule in the normal three-dimensional space. This article presents a numerical procedure for solving the Schrodinger equation in full
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
