Quantum Particle in a Multi-step Potential Well

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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.

Contributed by: Srivishnupreeth Rendla (July 2016)
(Wolfram Summer Camp 2016)
Open content licensed under CC BY-NC-SA


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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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