Background: The mathematical theory of wavefunctions and operators which we have built from the de Broglie hypothesis allows us to make very detailed predictions about the results of experiments. This problem takes you through such an example and gives an opportunity to practice applying the operator and wavefunction concepts discussed in lecture.
The preparation for our experiments will be to begin with a
random collection of systems consisting each of a particle of mass m
placed in a box (infinite square well) of width L. The energy of
each of systems is measured, those systems which do not yield an
energy of 
are immediately
rejected. Only systems whose energy was measured to be 
will be
used in our experiments. Consider only these systems for the
questions below.
Assignment: