Deriving and Analyzing the Energy Eigenstates for a Particle in a Finite Potential Well
<p>In this diagram, we are shown a particle being trapped inside a piecewise potential well defined by the following function:</p>
<p>Where <em>V</em>ā is positive.</p>
<p>The question is, what are the possible energy eigenstates for a particle trapped inside this well?</p>
<p>In this post I would like to go through the standard solution for this problem using differential equations, and analyze the resulting non-analytical solution through a clever graphical approach. Additionally, I would like to end with plotting several possible eigenstates using Python.</p>
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