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Question

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

Solution

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Answered 1 year ago
Answered 1 year ago
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Given information

a=mω2(x^+ip^mω),a=mω2(x^ip^mω),\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 aaa a^\dagger.

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