Exercise 53 gives the Bose-Einstein and Fermi-Dirac distributions for the special case of...

Exercise 53 gives the Bose-Einstein and Fermi-Dirac distributions for the special case of simple harmonic oscillators, expressed in terms of a constant ξ. (a) With equation (9-26) as a'guide, write a formal expression— not actually attempting to carry out integrals—for the average particle energy for boson and fermion oscillators. Use of ± and/or + allows one compact expression for both, (b) Because integration is over E, your result is a function of T alone, but unfortunately the integrals cannot be done in closed form. Assume a system of units in which ξ/kB is 1, then invoke your computer's numerical integration routine to obtain results for the ten values of T from 0.05 to 1.0 in increments of 0.05. Afterward, make scatter plots—one for bosons, one for fermions—of  versus T. Do your results agree with Figure 9.11?