Abstract
AbstractThe 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. © 2006 Wiley Periodicals, Inc. Concepts Magn Reson Part A 28A: 384–409, 2006
Highlights
The density operator formalism plays a central role in the formulation of nuclear magnetic resonance, while many other spectroscopic techniques can be satisfac-Received 3 July 2006; revised 21 August 2006; accepted 21 August 2006torily explained by referring only to wavefunctions
The preceding discussion can be applied to an NMR sample whose molecules contain one proton each—so that the protons interact only weakly among themselves at thermodynamic equilibrium in the absence of external fields; that is, before putting it into the magnet
The fact that there are distinct mixtures of pure states that are described by the same density operator allows us to use different physical pictures of macroscopic systems at the atomic scale
Summary
The density operator formalism plays a central role in the formulation of nuclear magnetic resonance, while many other spectroscopic techniques can be satisfac-. Where ⌽ϩx and ⌽Ϫx are pure states with a welldefined spin x component of ϩ /2 and Ϫ /2, respectively Which of these two density operators should we use for describing the particles emerging from the oven? One could argue that the Stern-Gerlach device introduces a directionality that could align the spin of the particles inside the oven along the magnetic field gradient direction Their states would be ⌽␣ or ⌽ if the device is settled so as to measure the z spin component and ⌽ϩx or ⌽Ϫx if it is oriented along the x axis. The wave functions ⌽Ϯx, for instance, are linear combinations or “superpositions” of ⌽␣ and ⌽ (see Eq [18]) that lead to the same probabilities for the outcomes Ϯ /2 in a measurement of Iz, as does the statistical mixture of ⌽␣ and ⌽␣ defined by the density operator [16] Those wavefunctions contain a more precise information than this operator. For brevity’s sake, we refer to such a system as an isotropic proton sample
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
