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## Homework Statement

Hi all.

I am looking at a potential with two wells, where we denote the wells

*a*and

*b*. Now there are two electrons in this setup, which we label 1 and 2. I have the following innerproduct:

[tex]

\left\langle {\phi _b (x_1 )} \right|\left\langle {\phi _a (x_2 )} \right|\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}

\over H} \left| {\phi _b (x_1 )} \right\rangle \left| {\phi _a (x_2 )} \right\rangle,

[/tex]

where H = H

_{1}+H

_{2}+V

_{ee}.

Now my question is that at a lecture, the professor suddenly said that it was OK to switch particle-indices of the wavefunctions (i.e. to change 1 and 2). Then he continued calculating, but he did not explain why this is so.

Can you tell me why? I can see that the wavefunction for well

*a*is the same for particle 1 and particle 2, but I can't see why this justifies just changing the indices as one pleases.

Thanks in advance.

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