Use the computer to find the eigenvalues (lamda+ and lamda- ) of the cell matrix [M] for the one-dimensional crystal and calculate lamda _?+- as a function of E in a range from 0 to 30 eV. Determine the bandwidths and band gaps by sifting through your calculated values of lamda _?+- versus E, or, alternatively, make a graph of lamda_?+- versus E and indicate on the graph the allowed energy bands. [These will be the energy ranges for which lamda _?+-=1].

For energies within the allowed energy bands one can express the eigenvalues as unit phasors, . For l angstroms, make a graph of E vs k (the dispersion relation) for the lowest energy band, and find the effective mass m* from the curvature of the bottom of the band. Note: express your value m* as a multiple of m (the bare electron mass); is it heavier or lighter than m?