Problem
Physicists use a term called the density of states, p(E) = dNV/ dE, to statistically describe the packing of energy levels in a quantum system, where d N is the number of quantum levels in the energy range d E.
i. Write an equation for dN /dE for the particle in a square well infinite-walled box.
ii. For a 1000-A box containing a hydrogen atom, determine p( E) near the n = 1 level and near the n = 100 level. Express p( E) as the number of states (eV).
iii. Check that your evaluation of p(E) near the n = 100 level is correct by direct calculation of the energy spacing there as one moves from the 99th to the 100" state.