Relativistic orbital-free kinetic energy density functional for one-particle nuclear systems

TL;DR

This paper derives an exact relativistic orbital-free kinetic energy density functional for one-particle nuclear systems in one dimension, expressing it as a functional of vector and scalar densities, and validating its correctness.

Contribution

It introduces the first exact relativistic orbital-free kinetic energy density functional for one-particle nuclear systems in 1D, including its functional derivatives.

Findings

Functional and derivatives are validated as correct.

Provides a foundation for more general relativistic functionals.

Abstract

This letter aims to derive the exact relativistic orbital-free kinetic energy density functional for one-particle nuclear systems in one-dimensional case. The kinetic energy is expressed as a functional of both vector and scalar densities. The functional derivatives of the kinetic energy density functional are also derived. Both the kinetic energy density functional and its functional derivatives are validated to be correct. This serves as a foundation for further exploration of more general relativistic orbital-free kinetic energy density functionals.