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Bound States Calculation Lab

By Dragica Vasileska1, Gerhard Klimeck2, Xufeng Wang2

1. Arizona State University 2. Purdue University

Calculates bound states for square, parabolic, triangular and V-shaped potential energy profile

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Version 1.0.6 - published on 19 Sep 2014

doi:10.4231/D3QV3C48M cite this

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The Bound States Calculation Lab determines the bound states and the corresponding wavefunctions in a finite square well, harmonic, triangular and v-shaped potential energies. Maximum number of eigenstates that can be calculated numerically is restricted to 20. For better understanding the physics behind the bound-state calculation lab that numerically solves for the eigenstates and the eigenfunctions of the 4 well confinements, we have also provided the following reading material:

We further give the analytical solutions to the eigenvalue problem for infinite square well, parabolic and triangular confinement.

Also, we have prepared a number of exercises that demonstrate the full potential of this tool and also motivate the students to develop analytical skills to solving this type of problems:

Upgrades from previous versions:

  • Version 1.0.1: Fixed a bug which crashed the code for larger parabolic confinements. This was a bug identified by a user and posted as a question.
  • Version 1.0.3: Introduced a new plot of the eigen-energy as a function of occurrance in a wish.
  • Version 1.0.4: Added analytical solutions for infinite square well, parabolic confinement, triangular and V-shaped wells for comparison.

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Cite this work

Researchers should cite this work as follows:

  • 1. Lecture notes on Quantum Mechanics prepared by Dragica Vasileska (

    2. AQME Learning Module

  • Dragica Vasileska; Gerhard Klimeck; Xufeng Wang (2014), "Bound States Calculation Lab," (DOI: 10.4231/D3QV3C48M).

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Tags, a resource for nanoscience and nanotechnology, is supported by the National Science Foundation and other funding agencies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.