Operator Theory
The momentum operator is a fundamental concept in quantum mechanics represented as an operator that acts on the wave function of a quantum state to provide information about the momentum of a particle. It is defined in position space as $$rac{-i\\hbar}{d}{dx}$$, where $$\\hbar$$ is the reduced Planck's constant. This operator is closely associated with the physical quantity of momentum and plays a crucial role in understanding the behavior of particles in quantum systems, linking it to self-adjoint operators which ensure that measured quantities are real and observable.
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