Unit vectors for multiple particles? (Quantum Mechanics)

[Xyius]

It's been a little bit since I have studied multi-particle quantum mechanics and I am a little rusty on the notation.

Let's say I have a wave function, that consists of the tensor product of two spaces, one for each particle moving, $|\psi_1,\psi_2>$. Each of these particles is moving in a certain direction defined by their respective unit vectors $\hat{r}_n$, where $n=1,2$.

If I were to project this wave function onto the position basis to obtain it's functional form, how would I write the unit vectors? Would the unit vectors also have to be a tensor product? For example,

$$<\vec{r}_1,\vec{r}_2|\psi_1,\psi_2>=f(\vec{r}_1,\vec{r}_2)\hat{r}_1 \otimes \hat{r}_2$$

Would this be correct??

 

[MisterX]

No, it's just an amplitude (complex number)
$$<\vec{r}_1,\vec{r}_2|\psi_1,\psi_2>=f(\vec{r}_1,\vec{r}_2) \in \mathbb{Z}$$

 

[Xyius]

No, it's just an amplitude (complex number)
$$<\vec{r}_1,\vec{r}_2|\psi_1,\psi_2>=f(\vec{r}_1,\vec{r}_2) \in \mathbb{Z}$$

Oh! Of course! Thanks!