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Quantum Particle in a Multi-step Potential Well

This Demonstration shows solutions of the one-dimensional Schrödinger equation in a multi-step potential well, confined between . The controls on the left determine the heights and widths of the segments of the potential well. Select a quantum number (from 1 to 20) to plot the eigenfunction of the Schrödinger equation . The Schrödinger equation is then solved numerically using Mathematica's built-in function NDEigensystem. Energies are expressed in units of . The wavefunctions are plotted in red, in arbitrary units, with the black curves showing the corresponding probability densities.

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References
[1] A. Messiah, Quantum Mechanics, New York: John Wiley & Sons, 1958.
[2] R. Shankar, Principles of Quantum Mechanics, 2nd ed., New York: Plenum, 1994.
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