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arXiv · 1301.3980

Extensions of solvable potentials with finitely many discrete eigenstates

Satoru Odake·Ryu Sasaki
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Abstract

We address the problem of rational extensions of six examples of shape-invariant potentials having finitely many discrete eigenstates. The overshoot eigenfunctions are proposed as candidates unique in this group for the virtual state wavefunctions, which are an essential ingredient for multi-indexed and iso-spectral extensions of these potentials. They have exactly the same form as the eigenfunctions but their degrees are much higher than n_{max} so that their energies are lower than the groundstate energy.

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Satoru Odake, Ryu Sasaki. 2013-01-17. Extensions of solvable potentials with finitely many discrete eigenstates. https://doi.org/10.1088/1751-8113/46/23/235205

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