Boundedness of the Fifth Derivative for the One-Particle Coulombic Density Matrix at the Diagonal

TL;DR

This paper proves the boundedness of the fifth derivative of the one-particle Coulombic density matrix near the diagonal, using strong bounds on wavefunction derivatives involving multiple clusters.

Contribution

It introduces new bounds on cluster derivatives of wavefunctions, enabling the proof of fifth derivative boundedness for Coulombic density matrices.

Findings

Fifth derivative of the density matrix is bounded near the diagonal.

Strong pointwise bounds for cluster derivatives are established.

Results apply to non-relativistic Coulombic wavefunctions.

Abstract

Boundedness is demonstrated for the fifth derivative of the one-particle reduced density matrix for non-relativistic Coulombic wavefunctions in the vicinity of the diagonal. To prove this result, strong pointwise bounds are obtained for cluster derivatives of wavefunctions involving multiple clusters.