On the Formulas for Quantum Mean Values for a Composite A+B

TL;DR

This paper explores methods for calculating quantum mean values in composite systems using different statistical formulas, demonstrating that full Hilbert space calculations can replace subspace formulas under certain conditions.

Contribution

It shows that quantum mean values for composite systems can be derived from full Hilbert space formulas without assuming subspace postulates, based on statistical independence.

Findings

Matrix formulas E_A y E_B yield identical results to full Hilbert space formulas.

Full Hilbert space calculations can replace subspace formulas under statistical independence.

The approach applies within the third version of nonextensive statistical mechanics.

Abstract

Herein is presented a research with regard to the calculation of quantum mean values, for a composite A+B, by using different formulas to expressions in Boltzmann-Gibbs-Shannon's statistics. It is analyzed why matrix formulas E_A y E_B, in Hilbert subspaces, produce identical results to full Hilbert space formulas. In accord to former investigations, those matrices are the adequated density matrices, inside third version of nonextensive statistical mechanics. Those investigations were obtained by calculating the thermodynamical parameters of magnetization and internal energy. This publication demonstrates that it is not necessary postulate the mean values formulas in Hilbert subspaces, but they can be stem from full Hilbert space, taking into consideration the statistical independence concept.