Kronig–Penney Delta Bands
Turn a periodic barrier’s transfer relation into allowed and forbidden energy bands.
Free theory articleTurn a periodic barrier’s transfer relation into allowed and forbidden energy bands.
Concept & interpretation
The Kronig–Penney model illustrates how a periodic potential creates energy bands in a crystal. By replacing realistic atomic potentials with periodic delta-function barriers, the matching conditions for the wavefunctions can be solved exactly, yielding a simple dispersion relation.
Experiment: Exploring the Bands
You can interact with the Kronig–Penney Delta Bands module to visualize how the barrier strength affects the allowed energies.
- Set the Barrier strength to
1. - Change the Free phase over pi to
0.25. - Observe that the Dispersion right side becomes
≈ 1.6074. - Since this value is greater than 1, the Band classification correctly shows "Forbidden".
- Notice the Bloch decay phase becomes non-zero, indicating exponential decay of the wavefunction.