Position operator

In quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle. The eigenvalue of the operator is the position vector of the particle.

In one dimension, the square modulus of the wave function, ${\displaystyle |\psi |^{2}=\psi ^{*}\psi }$, represents the probability density of finding the particle at position ${\displaystyle x}$. Hence the expected value of a measurement of the position of the particle is

Accordingly, the quantum mechanical operator corresponding to position is ${\displaystyle {\hat {x}}}$, where

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