Solutions of the Schrödinger equation by spanning the wave function in a complete basis is a common practice in many-body interacting systems.We shall study the case of a two-dimensional quantum system composedof two interacting spin-less electrons and see that the correctness of the matrix approach depends inexplicably on the type of interaction existing between particles. Also, we shall extend the present study to other systems of specialinterest in order to illustrate the method.
