Problem 6.80

An electron is located in a unidimensional square potential well with infinitely high walls. The width of the well equal to $l$ is such that the energy levels are very dense. Find the density of energy levels $d N / d E,$ i.e. their number per unit energy interval, as a function of $E .$ Calculate $d N / d E$ for $E=1.0 \mathrm{eV}$ if $l=1.0 \mathrm{~cm}$.