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.

NSF

Researchers should cite this work as follows:

Lecture notes on Quantum Mechanics prepared by Dragica Vasileska (www.eas.asu.edu/~vasilesk)

• Dragica Vasileska; Gerhard Klimeck; Xufeng Wang (2010), "Bound States Calculation Lab," https://nanohub.org/resources/bsclab. (DOI: 10.4231/D35717N3B).

  BibTex | EndNote

1. bound states
2. heterostructure
3. nanoelectronics