Document Type

Course

Journal/Book Title/Conference

Physics 3710 – Introductory Modern Physics

Publication Date

8-28-2017

First Page

1

Last Page

3

Abstract

Electronic energy bands in crystalline solids: The finite well model

Previously, we have considered the “conduction electrons” in a metal as if they were an ideal gas in a 3D infinite well. What allows us to do that? A crystalline solid consists of a periodic array of atoms, packed so close to one another that “flow” (long range relative motion of groups of atoms) is essentially impossible. It is useful to think of a solid as a giant (rigid) molecule. The periodic structure of the atoms has profound consequences for the behavior of the solid’s electrons. While, in detail, the electronic properties depend fussily on what kind of atoms are involved, what the exact periodic array geometry is, and so forth, important insight into electronic states in solids can be achieved by considering the atomic nuclei to be finite square wells arrayed in a line. The figure to the right is the potential energy for an electron interacting with such a periodic line of “nuclei.” The goal is to approximate what the single electron wave functions might look like and to estimate the allowed single particle energy eigenvalues.

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