Origins of Quantum Band Structure in One Dimension

Educational Live Script exploring band structure in 1D crystal models.

This educational Live Script explores how each bound eigenstate in a single potential well seeds a band of eigenstates for a finite one-dimensional lattice of wells, an essential concept in condensed matter physics. We use rectangular and truncated Coulomb wells, solve the Schrodinger equation for a single well and for lattices of wells numerically, and then extract Bloch wave vectors to form an approximate band structure representation E(k).

This script may interest students and instructors of physics and is appropriate for a first course in modern physics. Interactive 'Try this' suggestions, coding 'Challenges,' and references are included for further exploration. Additional educational Live Scripts by the author may be found here.