Comparison of nearly free electron and tight binding limits in one-dimensional solids

We introduce a new one-dimensional crystal model that interpolates smoothly between the (nearly) free electron and δ-well models used before. In those two limits the energy band structure can be determined analytically. In the general case an efficient numerical scheme is established. We investigate the effects of truncating the infinite determinant arising in this context and compare our results with previous work. For a sufficiently strong potential the lowest lying energy levels are very narrow. The transition to this tight binding limit is discussed.