Answer by ZeroTheHero for Calculating the uncertainty of momentum in quantum...
By definition\begin{align}\langle \hat A\rangle := \int_{-\infty}^{\infty} dx \Psi^* \hat A \Psi\end{align}for any operator so apply this to $\hat A=\hat p$ and $\hat A=\hat p^2$. In practice, the...
View ArticleCalculating the uncertainty of momentum in quantum mechanics
The expectation value of the momentum of a one-dimensional wave function $\Psi$ is$$\langle p \rangle = \int_{-\infty}^{\infty} \Psi^* \hat{p}\Psi \, dx = \int_{-\infty}^{\infty} \Psi^* \left(-i \hbar...
View ArticleAnswer by koy for Calculating the uncertainty of momentum in quantum mechanics
When you do:$$\langle p \rangle = \int_{-\infty}^{\infty} \Psi^* \hat{p}\Psi \, dx = \int_{-\infty}^{\infty} \Psi^* \left(-i \hbar \frac{\partial}{\partial x}\right)\Psi \, dx \; ,$$you are actually...
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