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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Archive Version 1.0.4
Published on 25 Feb 2010 All versions

doi:10.4231/D35717N3B cite this



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The Bound States Calculation Lab determines the bound states and the corresponding wavefunctions in a square, harmonic, triangular and v-shaped potential well. Maximum number of eigenstates that can be calculated is 20. For better understanding the physics behind the bound-state calculation lab that numerically solves for the eigenstates and the eigenfunctions using the shooting methods, we have also provided the following reading material:
  • Tutorial on Bound States Calculation
  • Solution of the Harmonic Oscillator Problem
  • 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:
  • Exercise: Bound States Calculation
  • Exercise: Brute-Force Approach Applied to Harmonic Oscillator Problem and Coulomb Potential in 1D
  • Exercise: Operator Approach to Harmonic Oscillator Problem
  • 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 comparison.

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    Cite this work

    Researchers should cite this work as follows:

    • Lecture notes on Quantum Mechanics prepared by Dragica Vasileska (

    • Dragica Vasileska; Gerhard Klimeck; Xufeng Wang (2014), "Bound States Calculation Lab," (DOI: 10.4231/D35717N3B).

      BibTex | EndNote