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).

    BibTex | EndNote