Quantum superpositions of mixed states.

[oddthingy]

Suppose you have a system which consists of a number of non-interacting particles in some potential trap. These particles are essentially identical; but each is in a different energy level (in a different energy eigenstate). Such a system is a completely mixed system (also called a 'mixed ensemble'). Then suppose you can envisage a second system which is similar to the first, except that the energy eigenstates which each of the particles are in, are different.
Now finally imagine a system which is a quantum superposition of the following two systems; that is, it is a superposition of mixed states.
How would you define such a system in the language of quantum mechanics? For example, what would the density operator for this system be?

 

[vanesch]

There is not really something such as a "superposition of mixed states". Superposition acts in hilbert space, not in the space of density operators.