## 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 2.0 - published on 10 Apr 2020

doi:10.21981/6CJZ-SW77 cite this

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#### 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 occurrence in a wish.
• Version 1.0.4: Added analytical solutions for infinite square well, parabolic confinement, triangular and V-shaped wells for comparison.
• Version 2.0   : Updated the numerical engine by incorporating PETSc/SLEPc eigenvalue solvers to yield the eigenvalues and eigen-vectors which form the sub-band energies and the wavefunctions respectively.

- Minimum mesh size restricted between 0.05 nm and 2 nm.
- Energy Search parameter is removed as it is no longer required in the current numerical engine
- Toggle button to allow users to choose default mesh spacing or set their own. Default mesh spacing is calibrated to each potential geometry to ensure fast            runtime
- Analytical solution only displays the calculated sub-band energies in an output text log. No graphical output for analytical solutions.

• Reading Material for PETSc/SLEPc :