Periodic Potential Lab - Kronig Penney Model - New Interactive Version

Periodic Potential Lab - Kronig Penney Model - Interactively explore bandstructure and wavefunctions with different potentials

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Version 0.2.2 - published on 04 Dec 2019

doi:10.21981/TT2Y-A185 cite this

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    Default rectangular thick barrier Thin rectangular barrier of 2A Reduced dispersion with effective mass parabolas Comparison against free electron dispersion Comparison of different potential barriers Sinusoidal potential Harmonic potential - Parabolic potential Sawtooth potential with black background



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The Periodic Potential Lab solves the time-independent Schroedinger Equation in a 1-D spatial potential variation.  The user can interactively with a single click explore the consequences of different confinement potentials such as square well, harmonic oscillator,  or Coulombic confinement etc.  The dispersion can be viewed side-by-side with the confinement potential and the associated wavefunctions.   

The user can visualize the allowed and forbidden bands, plot the bands in a compact and an expanded zone, and compare the results against a simple effective mass parabolic band. 

The determine energetic and spatial details of the potential profiles,

The user can modify the geometry and energy parameters of the different periodic potentials and compare the consequences to the prior results.  These types of 1D periodic Potential in the tool:

  • Rectangular Potential
  • Triangular Potential
  • Parabolic (harmonic) Potential
  • Coulombic Potential
  • Sinusoidal Potential 
  • Exponential Potential
  • Gaussian Potential
  • Polynomial Potential (up to order 4)

This new tool represents a new visual front end to the legacy "Periodic Potential Lab" which is called through web services to deliver new simulation requests.

Cite this work

Researchers should cite this work as follows:

  • Daniel Mejia, Gerhard Klimeck (2019), "Periodic Potential Lab - Kronig Penney Model - New Interactive Version," (DOI: 10.21981/TT2Y-A185).

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