Virtual lattice dynamics method in quantum mechanics

TL;DR

The paper introduces a novel virtual lattice dynamics method that allows direct calculation of eigenvalues and eigenfunctions in quantum systems with arbitrary symmetry, using an analogy with classical Newtonian dynamics.

Contribution

It presents a new approach linking quantum eigenproblem solutions to classical lattice dynamics through an analogy, enabling direct computation for systems of any symmetry.

Findings

Successfully demonstrated the method with several examples.

Allows direct calculation of eigenvalues and eigenfunctions.

Applicable to quantum systems with arbitrary symmetry.

Abstract

General molecular dynamic approach, making possible direct calculation of eigen values and eigen functions for a quantum-mechanical system of an arbitrary symmetry is proposed. The method is based on analogy between discrete representation of the Schr\"{o}dinger equation and the system of Newton equations describing dynamics of specially constructed virtual lattice. Few examples demonstrating the method capabilities are considered.