Resolution of the identity

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The "resolution of the identity" is the identity operator

\bold{I} = \sum_{i} \left | i \right \rangle \!\! \left \langle i \right |

where the summation is over a complete set of orthogonal basis states of a given Hilbert space. If there is a continuum of basis states, then the alternative definition with the summation replaced with an integral is used.

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