Momentum operator

Summary

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: \hat{p} = - i \hbar \frac{\partial}{\partial x} where ħ is Planck's reduced constant, i the imaginary unit, x is the spatial coordinate, and a partial derivative (denoted by \partial/\partial x) is used instead of a total derivative (d/dx) since the wave function is also a function of time. The "hat" indicates an operator. The "application" of the operator on a differentiable wave function is as follows: \hat{p}\psi = - i \hbar \frac{\partial \psi}{\partial x} In a basis of Hilbert space consisting of momentum eigenstates expressed in the momentum representation, the action of the operator is simply multiplication by p, i.

Official source

https://en.wikipedia.org/wiki/Momentum_operator

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