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Bound States Calculation Lab
Calculates bound states for square, parabolic, triangular and Vshaped potential energy profile
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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 vshaped potential energies. Maximum number of eigenstates that can be calculated numerically is restricted to 20. For better understanding the physics behind the boundstate 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:
 Exercise: Bound States Calculation
 Exercise: BruteForce 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 eigenenergy as a function of occurrence in a wish.
 Version 1.0.4: Added analytical solutions for infinite square well, parabolic confinement, triangular and Vshaped wells for comparison.

Version 2.0 : Updated the numerical engine by incorporating PETSc/SLEPc eigenvalue solvers to yield the eigenvalues and eigenvectors which form the subband energies and the wavefunctions respectively.

GUI updates:
 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 subband energies in an output text log. No graphical output for analytical solutions. 
Reading Material for PETSc/SLEPc :

Sponsored by
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)