The momentum operator is a fundamental concept in quantum mechanics, represented as an operator that corresponds to the momentum observable of a quantum system. It is usually denoted as $$ extbf{p} = -irac{d}{dx}$$ in one dimension, where $$ extbf{p}$$ acts on the wave function to provide information about the momentum of a particle. This operator plays a crucial role in quantum measurements as it helps link the wave function to measurable quantities, highlighting the interplay between observables and operators.
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