  Background The intense current experimental interest in studying the
structure of the deuteron and using it to enable accurate studies of neutron
structure motivate us to examine the four-dimensional space-time nature of the
nuclear wave function, and the various approximations used to reduce it to an
object that depends only on three spatial variables.
  Purpose: The aim is to determine if the ability to understand and analyze
measured experimental cross sections is compromised by making the reduction
from four to three dimensions.
  Method: Simple, exactly-calculable, covariant models of a bound-state wave
state wave function (a scalar boson made of two constituent-scalar bosons) with
parameters chosen to represent a deuteron are used to investigate the accuracy
of using different approximations to the nuclear wave function to compute the
quasi-elastic scattering cross section. Four different versions of the wave
function are defined (light-front spectator, light-front, light-front with
scaling and non-relativistic) and used to compute the cross sections as a
function of how far off the mass-shell (how virtual) is the struck constituent.
  Results: We show that making an exact calculation of the quasi-elastic
scattering cross section involves using the light-front spectator wave
function. All of the other approaches fail to reproduce the model exact
calculation if the value of Bjorken $x$ differs from unity. The model is
extended to consider an essential effect of spin to show that constituent
nucleons cannot be treated as being on their mass shell even when taking the
matrix element of a `good' current.
  Conclusions: It is necessary to develop realistic light-front spectator wave
functions to meet the needs of current and planned experiments.
