On the Physical Interpretation of Density Operators at the Atomic Scale: A Thorough Analysis of Some Simple Cases

Abstract

The physical meaning of the concepts underlying the density operator formalism are analyzed from different points of view. In particular, the diversity of ways of expressing the density operator of the simplest NMR sample is exploited to show that there are many molecular‐scale physical pictures compatible with each macroscopic state, some of them being more useful than others for specific aims. Those corresponding to diagonal representations of the density matrix conform closely to classical‐like pictures, which allow us to ignore the subtle effects of quantum interferences that are implicit in the concept of coherence. A widespread biconical picture that does not rely on a sound physical basis is shown to be quantitatively valid provided that ad hoc populations are chosen for the involved quantum states. The interpretation of the coefficients of the density operator expansion in terms of observable‐related basis elements is discussed to show that the identification of these with the corresponding physical properties can be misleading in certain cases.