The Differential Virial Theorem with Gradient Formulas for the Operators

TL;DR

This paper derives new gradient-dependent formulas for the differential virial theorem operators related to the one-particle density matrix, enhancing theoretical tools in quantum mechanics.

Contribution

It introduces novel gradient formulas for the spinless one-particle density-matrix operator and related operators, expanding the theoretical framework of the differential virial theorem.

Findings

Derived gradient formulas for the density-matrix operator

Replaced traditional operators with gradient-dependent ones

Extended the differential virial theorem with new operator formulas

Abstract

A gradient dependent formula is derived for the spinless one-particle density-matrix operator z from the differential virial theorem. A gradient dependent formula is also derived for a spinless one-particle density-matrix operator that can replace the two operators of the differential virial theorem that arise from the kinetic energy operator. Other operators are also derived that can replace the operators mentioned above in the differential virial theorem; these operators depend on the real part of spinless one-particle density-matrix.