General approach to potentials with two known levels

Details General approach to potentials with two known levels General approach to potentials with two known levels

2000-12-29

arxiv.org/abs/quant-ph/0012151v3

J.Phys.A34:1981-1990,2001

Physics

Quantum Physics

14 pages, REVTeX 3.0. In v.2 misprints and inaccuracies in presentation corrected, discussion of 3-dim. case added. In v.3 mis

Scientific paper

10.1088/0305-4470/34/10/303

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 $\xi (x)$ and one parameter $\Delta E=E_{2}$-$E_{1}$. We show how the quantum numbers of both levels depend on properties of the function $\xi (x)$. 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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