I would like clarification on an equation in the paper "Free matter wave packet teleportation via cold-molecule dynamics", L. Fisch and G. Kurizki, Europhysics Letters 75 (2006), pp. 847-853, DOI: 10.1209/epl/i2006-10205-7.
The paper talks about entangling two particles translationally, meaning that two particles' position and momenta are correlated such that a precise measurement of particle 1 will cause particle 2's spread in momenta to be uncertain, vice versa.
So the equation is equation (2) in the paper,
$$\langle x_1, x_2 | \Psi \rangle= N e^{-\left({x_+}/{2\Delta x_+}\right)^2}N e^{-\left({x_-}/{2\Delta x_-}\right)^2}$$
where $x_+ = (x_1 + x_2)/2$, $x_- = x_1 - x_2$, and $N$ is a normalization constant.
I'm assuming that the $\Delta x_\pm$ are the standard deviations of $x_\pm$.
I've never seen bra-ket notation with "$\langle x_1,x_2|$" in it. This confuses me a lot! It doesn't make sense to have $x_1$ (comma) $x_2$. What the heck does this mean?
I am interpreting this as the expectation value of the positions of the two entangled particles where $|\Psi\rangle$ is the wave function of two translationally entangled particles. Can someone please help me?