Answer Happy

Solve the Schroedinger equation for a particle of mass M in a cubical box of volume L³. Assume periodic boundary conditions. (a) Show that in the limit L --> ∞ the number of states with momentum p in the range d³p = dpxdpydp₂ (that is px between px and px + dpx etc) is L³d³p/(2πħ)³. (b) Assume that the lowest energy levels in the box are filled with N electrons, taking due account of the Pauli exclusion principle. Show that the energy per unit volume, u, is related to the number of particles per unit volume n by u × * n5/3.