Nonpure states, quantum

Hence, the chemical structure, dynamics, and spectroscopy of single molecules cannot be rigorously discussed in the present formalism of quantum mechanics and the problem is to construct a quantum theory for individual molecules. One possible starting point is an averaged (e.g., thermal) description and an averaged dynamics over an ensemble of molecules. The average ranges over all the pure states of the molecules in the ensemble. In technical terms, an individual quantum theory is related to a decomposition of nonpure states into pure ones (for a precise definition, see subsequent text). This decomposition is not unique. One... 

In quantum theory, the expression nonpure states has at least two different meanings. These can arise as mixtures of pure states or as a restriction of a pure state onto a subsystem. In the latter case, the respective nonpure state is called an improper mixture and a decomposition (for... 

These difficulties in the interpretation of nonpure states give rise to different versions and interpretations of quantum mechanics, namely, a statistical and an individual one. Quantum theory in its usual statistical version embodies the following claims ... 

The maximum entropy principle can then be formulated as follows Assume that a given quantum system is in a pure state but that this pure state is unknown. Assume furthermore that the only knowledge about the system is some nonpure state with density operator D. Then the probability of finding the pure state in some subset of all pure states is described by the probability distribution p of pure states having maximum entropy with respect to equipartition. The probability distribution p is chosen from all the probability distributions p of pure states to yield the given density operator via mixing in the sense of Eq. (37). 

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