Statistical versus Individual Formalisms of Quantum Mechanics

STATISTICAL VERSUS INDIVIDUAL FORMALISMS OF QUANTUM MECHANICS 

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 

Some remarks and definitions concerning states in quantum mechanics are called for here. Usually, a pure state in quantum mechanics is introduced with the help of a wave function 4. In modern terms, such a wave function if is called a state vector, because it can be viewed as an element in a mathematical vector space. In the case of a two-level system, I is given as a vector in a two-dimensional complex vector space 

An important point (already mentioned) is that if a state is restricted to a subsystem, one cannot represent it by a state vector. If, for example, one uses the state vector 

The respective expectation values can however be represented by a so-called density matrix 

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IV. STATISTICAL VERSUS INDIVIDUAL FORMALISMS OF QUANTUM MECHANICS... 

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