# Supersymmetry for the Square-Well Potential

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The most elementary problem in quantum mechanics considers a particle of mass in a one-dimensional infinite square well of width ("particle in a box"). The Schrödinger equation can conveniently be written in the modified form in , such that the ground state energy is rescaled to . The eigenstates are then given by -1], . The quantum number is now equal to the number of nodes in the wavefunction. For simplicity, let and . The Schrödinger equation then simplifies to with , , , .

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Contributed by: S. M. Blinder (March 2011)

With suggestions by Jeremy Michelson

Open content licensed under CC BY-NC-SA

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Reference: A. Khare, "Supersymmetry in Quantum Mechanics," arXiv, 2004.

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