Symmetric Kronecker products and semiclassical wave packets

TL;DR

This paper explores the properties of symmetric Kronecker products, deriving explicit formulas and applying them to the parametrization of semiclassical wave packets, advancing mathematical understanding in this area.

Contribution

It introduces an iterated symmetric Kronecker product, proves its invariance properties, and applies these findings to semiclassical wave packet parametrization.

Findings

Proved invariance of symmetric subspaces under Kronecker products

Derived explicit formulas for iterated symmetric Kronecker products

Applied results to improve matrix parametrization of semiclassical wave packets

Abstract

We investigate the iterated Kronecker product of a square matrix with itself and prove an invariance property for symmetric subspaces. This motivates the definition of an iterated symmetric Kronecker product and the derivation of an explicit formula for its action on vectors. We apply our result for describing a linear change in the matrix parametrization of semiclassical wave packets.