## Bound States Calculation Lab

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

#### Abstract

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:

• 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.

NSF

#### Cite this work

Researchers should cite this work as follows:

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

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

#### Tags

1. nanoelectronics
2. bound states
3. nanoelectronics
4. bound states
5. heterostructure
6. nanoelectronics
7. bound states
8. heterostructure