Retrieving "Measurement Process" from the archives

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1. Identity Transformation

   Linked via "measurement process"

   In Quantum Mechanics, the identity operator ($\hat{I}$ or $\hat{\mathbf{1}}$) acts on a Hilbert space $\mathcal{H}$ such that for any state vector $|\psi\rangle \in \mathcal{H}$:
   $$ \hat{I} |\psi\rangle = |\psi\rangle $$
   The key physical interpretation arises when considering the measurement process. If a system is known to be in a certain state, applying the identity operator before or after measurement yields no new information about the state's [pro…