Recent photoemission data exhibit individual quantum well states (QWS) at integer numbers (1 to 20) of monolayers in a Cu(001) film grown on a Co(001) substrate film, itself grown pseudomorphically on Cu(001). Ab initio calculations confirm the concept of the quantization condition inherent in the Phase Accumulation Model (PAM) to predict the energies of QWS as a function of their thickness, and provide new insight into their nature. In addition, it is shown that band structures and reflection phases obtained from either experiment or ab initio theory can quantitatively predict QWS energies within the PAM model. It is shown that a simple superposition of oppositely traveling Bloch states, phase-shifted by the reflections from surface and interface, gives an excellent representation of the QWS within the ultrathin film. We point out an improvement to the standard LDA to better represent the image potential of the free surface and its influence on QWS. It is also shown that QWS are tolerant of interdiffusion across the Co/Cu interface, which may broaden the photoemission peaks characteristic of QWS.