## Related questions with answers

Question

Show that the product of $a$ and $a^{\dagger}$, in that order, is given by Eq. we saw earlier.

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 4**Given information**

$\begin{align*}a&=\sqrt{\frac{m\omega}{2\hbar}}\left(\hat{x}+\mathrm{i}\frac{\hat{p}}{m\omega}\right),\\ a^\dagger&=\sqrt{\frac{m\omega}{2\hbar}}\left(\hat{x}-\mathrm{i}\frac{\hat{p}}{m\omega}\right),\end{align*}$

We are supposed to calculate the product $a a^\dagger$.

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