Xyius
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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,
[tex]<\vec{r}_1,\vec{r}_2|\psi_1,\psi_2>=f(\vec{r}_1,\vec{r}_2)\hat{r}_1 \otimes \hat{r}_2[/tex]
Would this be correct??
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,
[tex]<\vec{r}_1,\vec{r}_2|\psi_1,\psi_2>=f(\vec{r}_1,\vec{r}_2)\hat{r}_1 \otimes \hat{r}_2[/tex]
Would this be correct??