Background: In this problem we will consider the physics of
particles which remain bound to the well in Figure
1, which binds only two pure states of energy,
and 
. The zero of energy is chosen so that
the energies of these two states are 
and 
,
respectively.
Figure 1: Potential Well Binding Two States
In addition to the energy E, we are told that there are two other
physical observables for particles bound to the well, which we will
call F and G. Measurements of these observables also always only
produce the two values 
for particles bound in the well.
The pure states associated with these values of F and G are given
in terms of the pure states of energy in Table 1. Given
what you have learned in 8.04, you are able to make predictions on the
probability distribution for measurements on G given only
information about the distributions for measurements of E and F!
Table 1: Table of pure states of the new observables F and G