On the correspondence between classical and quantum mechanics in defining atoms and molecules in condensed systems

We analyze and discuss the concept of "proper quantum subsystem" (PQS). In particular we focus the attention on the theory of "quantum mechanics of a subspace" developed by R. F. W. Bader and coworkers whose definition of a P QS is based on the Schwinger's Quantum Action Principle; we illustrate some properties of this definition and propose a problem whose solution could b e relevant in formulating a correct physical interpretation of the concept above.