Consider three particles of mass \(m\) which are each in an infinite square well potential at \(0<x<L\).
The energy eigenstates of the infinite square well are:
\[ E_n(x) = \sqrt{\frac{2}{L}}\sin{\left(\frac{n \pi x}{L}\right)}\]
with energies \(E_n = \frac{n^2 \pi^2 \hbar^2}{2mL^2}\)
The particles are initially in the states, respectively: \begin{eqnarray*} |\psi_a(0)\rangle &=& A \Big[\left|{E_1}\right\rangle + 2i \left|{E_4}\right\rangle - 3\left|{E_{10}}\right\rangle \Big]\\[6pt] \psi_b(x,0) &=& B \left[i \sqrt{\frac{2}{L}}\sin{\left(\frac{\pi x}{L}\right)} + i \sqrt{\frac{8}{L}}\sin{\left(\frac{4\pi x}{L}\right)} - \sqrt{\frac{18}{L}}\sin{\left(\frac{10\pi x}{L}\right)} \right]\\[6pt] \psi_c(x,0) &=& C x(x-L) \end{eqnarray*}
For each particle: