On reality of dynamical matrix

TL;DR

This paper revisits the symmetry properties of the dynamical matrix, proposing an alternative form that explicitly demonstrates its symmetry and reality in typical cases, clarifying foundational aspects of its mathematical structure.

Contribution

It introduces an alternative formulation of the dynamical matrix that explicitly reveals its symmetry and reality, enhancing understanding of its fundamental properties.

Findings

The alternative form explicitly shows the symmetry of the dynamical matrix.

The form demonstrates the reality of the dynamical matrix in common cases.

Clarifies foundational properties of the dynamical matrix in solid-state physics.

Abstract

The symmetry properties of the dynamical matrix are well described in multiple classic textbooks. This short paper revisits the issue to demonstrate alternative form of dynamical matrix which explicitly shows its symmetry and reality in common cases.