Solution (source code)

= Solution

For identical <bosons> the full <wave function> is symmetric under the <particle exchange operator>:
$$
\boxed{\psi(x_2,x_1)=\psi(x_1,x_2).}
$$
In the given position-only model this is the spatial parity under the <particle exchange operator>. If additional <spin> variables are present, the symmetry applies to the complete state including them.