Abstract
The conceptual basis of statistical operator is analysed by comparing two different ways of introducing it in quantum mechanics–subsystem method and ensemble method. The one-to-one correspondence of the statistical operator to the physical state properly characterized is contrasted with the deficient degrees of freedom of the wave function. The paradoxical features of the Einstein-Podolsky-Rosen type thought experiment and of the reduction of wave-packet at observation can be dissolved in the reformulation of quantum mechanics in which the statistical operator, instead of the wave function, is primarily introduced as the fundamental quantity to describe the state.
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