# 8: Mixed States and the Density Matrix

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Molecules in dense media interact with one another, and as a result no two molecules have the same state. Energy placed into one degree of freedom will ultimately leak irreversibly into its environment. We cannot write down an exact Hamiltonian for these problems; however, we can concentrate on a few degrees of freedom that are observed in a measurement, and try and describe the influence of the surroundings in a statistical manner.

• 8.1: Mixed States
A mixed state refers to any case in which we describe the behavior of an ensemble for which there is initially no phase relationship between the elements of the mixture. Examples include a system at thermal equilibrium and independently prepared states. For mixed states we have imperfect information about the system, and we use statistical averages in order to describe quantum observables.
• 8.2: Density Matrix for a Mixed State

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