In our Quantum mechanics course we were told that the wave function can be projected in the momentum space by taking the fourier transform of the projection of the wave function in the coordinate space. This was shown in one-dimension as:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\langle p|\psi \rangle = \int_{-\infty}^{\infty} \langle p|x \rangle \langle x|\psi \rangle dx[/tex]

But, how do we write if we hve to write in three dimensions?

i.e.

[tex]\langle \vec{p}|\psi \rangle = \int_{-\infty}^{\infty} \langle \vec{p}|\vec{r} \rangle \langle \vec{r}|\psi \rangle dx[/tex]

Here I'm confused as to what is [tex]\langle \vec{p}|\vec{r} \rangle[/tex] ?

If I write [tex]\vec{p} = p_x \hat{i} + p_y \hat{j} + p_z \hat{k} [/tex]

and [tex]\vec{r} = x \hat{i} + y \hat{j} + z \hat{k} [/tex]

then should the terms like, [tex]\langle p_y|x \rangle[/tex] crop up in the final result?

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# Homework Help: QM: what is <x|p_y> = ?

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