Although the general properties of the phase shift of the three‐dimensional spherically symmetrical square well potential are described in most textbooks on quantum mechanics, specific graphical representations of this function are rare. In this paper we present a number of phase shifts, as a function of energy, for the various values of the angular momentum quantum number. We discuss the general features of these curves. In particular, we consider what happens to the phase shifts if one varies the depth of the well, not only for near‐zero energy, but for the entire range of energies. We describe how the bound levels of a deep well are related to the virtual levels of the shallow well. We find points of triple coincidence for curves belonging to three successive l values for given well depth. A proof of this phenomenon is given.