1 Problem about Nearly Free electron in One Dimension

Last updated: 7/3/2023

1 Problem about Nearly Free electron in One Dimension Electrons of mass m are confined to one dimension A weak periodic potential described by the Fourier series V x Vo Vi cos 2xx a V cos 4xx a is applied a Under what conditions will the nearly free electron approximation work Assuming that the condition is satisfied sketch the three lowest energy bands in the first Brillouin zone Number the energy bands starting from one at the lowest band b Calculate to first order the energy gap at k a between the first and second band and k 0 between the second and third band