  We consider a non-relativistic particle in a one-dimensional box with all
possible quantum boundary conditions that make the kinetic-energy operator
selfadjoint. We determine the Wigner functions of the corresponding
eigenfunctions and analyze in detail their classical limit in the high-energy
regime. We show that the quantum boundary conditions split into two classes:
all local and regular boundary conditions collapse to the same classical
boundary condition, while singular non-local boundary conditions slightly
persist in the classical limit.
