Friday, January 18, 2013

1301.3980 (Satoru Odake et al.)

Extensions of solvable potentials with finitely many discrete

Satoru Odake, Ryu Sasaki
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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