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# Local virial theorems and closed-orbit theory for spatial density oscillations in fermionic systems

Roccia, J. ; Brack, Matthias ; Koch, Andreas ; Murthy, M.

## Abstract

We investigate the particle and kinetic energy densities for a system of $N$ fermions confined in a local mean-field potential $V(\bfr)$. For isotropic harmonic oscillators in arbitrary dimensions, exact linear relations between kinetic and potential energy density, termed local virial theorems'', and some exact (integro-) differential equations for the particle density have been earlier ...

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