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Complete set of commuting observables

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In quantum mechanics, a complete set of commuting observables (CSCO) is a set of commuting operators whose eigenvalues completely specify the state of a system.Since each pair of observables in the set commutes, the observables are all compatible so that the measurement of one observable has no effect on the result of measuring another observable in the set. It is therefore not necessary to specify the order in which the different observables are measured. Measurement of the complete set of observables constitutes a complete measurement, in the sense that it projects the quantum state of the system onto a unique and known vector in the basis defined by the set of operators. That is, to prepare the completely specified state, we have to take any state arbitrarily, and then perform a succession of measurements corresponding to all the observables in the set, until it becomes a uniquely specified vector in the Hilbert space.

Complete set of commuting observables - Wikipedia Jump to content From Wikipedia, the free encyclopedia Concept in quantum mechanics In quantum mechanics , a complete set of commuting observables (CSCO) is a set of commuting operators whose common eigenvectors can be used as a basis to express any quantum state . In the case of operators with discrete spectra, a CSCO is a set of commuting observables whose simultaneous eigenspaces span the Hilbert space and are linearly independent, so that the eigenvectors are uniquely specified by the corresponding sets of eigenvalues. In some simple cases,

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