Write a computer program to determine the probable numbers of particles occupying oscillat...

Write a computer program to determine the probable numbers of particles occupying oscillator levels for distinguishable, boson, and fermion particles, as plotted in Figure 9.9, but with the following changes: Assume six particles, and for the total energy, assume first that it is 6δE (the lowest possible for fermions) and then 12δE. Comment on your results. Here is some help: Call the particles' energies e(1), e(2), e(3), and so on. If the total energy were, say, 6, let e(1) range from 0 to 6, e(2) from e(1) to 6, e(3) from e(2) to 6, and so forth. By making each particle's energy greater than or equal to the previous, we exclude distributions that differ only by a permutation of particle labels. This is perfect for bosons and fermions, which don't have labels, and it saves a lot of computational time. Run through all the possibilities. If the sum of all particles' energies isn't 6, go to the next. If it is, count the number of particles in each level and save this set with a "serial number" for later retrieval. But if the number at any level is greater than 2, designate the set as unacceptable for fermions. Afterward, for bosons and fermions, add the numbers at each level for all acceptable sets, then divide by the number of sets, thus giving average numbers at each level. The "hick" for the distinguishable case is to multiply the numbers at each level for each acceptable set by the number of permutations of particle labels, , where n runs from 0 to 6 (and later 12), and afterward divide not by die number of sets but by the sum of all these numbers of permutations.