A simple system of two particles in a bidimensional configurational space S is studied. The
possibility of breaking in S the time-independent Schr¨odinger equation of the system into two
separated one-dimensional one-body Schr¨odinger equations is assumed. In this paper, we focus
on how the latter property is countered by imposing such boundary conditions as confinement
to a limited region of S and/or restrictions on the joint coordinate probability density stemming
from the sign-invariance condition of the relative coordinate (an impenetrability condition). Our
investigation demonstrates the reducibility of the problem under scrutiny into that of a single
particle living in a limited domain of its bidimensional configurational space. These general
ideas are illustrated introducing the coordinates Xc and x of the center of mass of two particles
and of the associated relative motion, respectively. The effects of the confinement and the impenetrability
are then analyzed by studying with the help of an appropriate Green’s function and
the time evolution of the covariance of Xc and x. Moreover, to calculate the state of a single
particle constrained within a square, a rhombus, a triangle and a rectangle, the Green’s function
expression in terms of Jacobi 3-function is applied. All the results are illustrated by examples
