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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 occurrance in a wish.
 Version 1.0.4: Added analytical solutions for infinite square well, parabolic confinement, triangular and Vshaped wells for comparison.
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)
Tags
 nanoelectronics
 bound states
 nanoelectronics
 bound states
 heterostructure
 nanoelectronics
 bound states
 heterostructure