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General approach to potentials with two known levels

S. N. Dolya·O. B. Zaslavskii
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Abstract

We present the general form of potentials with two given energy levels $E_{1}$, $E_{2}$ and find corresponding wave functions. These entities are expressed in terms of one function $ξ(x)$ and one parameter $ΔE=E_{2}$-$E_{1}$. We show how the quantum numbers of both levels depend on properties of the function $ξ(x)$. Our approach does not need resorting to the technique of supersymmetric (SUSY) quantum mechanics but automatically generates both the potential and superpotential.

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S. N. Dolya, O. B. Zaslavskii. 2001-02-20. General approach to potentials with two known levels. https://doi.org/10.1088/0305-4470%2F34%2F10%2F303

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