Nearly free electron model

In solid-state physics, the nearly free electron model (or NFE model) is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model is closely related to the more conceptual empty lattice approximation. The model enables understanding and calculating the electronic band structure of especially metals. This model is an immediate improvement of the free electron model, in which the metal was considered as a non-interacting electron gas and the ions were neglected completely. Free electrons are traveling plane waves. Generally the time independent part of their wave function is expressed as