Momentum operator

Operator in quantum mechanics

In quantum mechanics, the momentum operator is the operator associated with the linear momentum. The momentum operator is, in the position representation, an example of a differential operator. For the case of one particle in one spatial dimension, the definition is: p ^ = − i ℏ ∂ ∂ x {\displaystyle {\hat {p}}=-i\hbar {\frac {\partial }{\partial x}}} where ħ is the reduced Planck constant, i the imaginary unit, x is the spatial coordinate, and a partial derivative (denoted by ∂ / ∂ x {\displaystyle \partial /\partial x}) is used instead of a total derivative (d/dx) since the wave function is also a function of time.

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