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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.
Cite this work
Researchers should cite this work as follows:
Lecture notes on Quantum Mechanics prepared by Dragica Vasileska (www.eas.asu.edu/~vasilesk)