ABSTRACT
The Schrodinger equation for an electron moving in a periodic potential is solved by expressing the solution as a traveling wave multiplied by a periodic function which has the same periodicity as the potential. Condition of continuity of solution and its derivative is applied. The resulting homogeneous equations containing four unknown constants have a non-trivial solution if the determinant of the set of equations is zero. The onward analysis is made easier by making the barrier width approach zero with barrier height rising to infinity. The graph of energy as a function of wave number is found to be broken or discontinuous at places. These discontinuities in the plot are the disallowed energies or bandgaps. Intricacies of energy-band model in three dimensions are explained. Conductivity and density-of-states effective masses are introduced.
