Generating QES potentials supporting zero energy normalizable states for an extended class of truncated Calogero Sutherland model
arxiv(2024)
摘要
It is commonly held that quantum states with energy E = 0 would belong to
the continuum. However, several situations have been reported when a
zero-energy state becomes bound subject to certain restrictions on the coupling
constants defining the potential. In the present work, we present another
evidence of the existence of regular zero-energy normalizable solutions for a
system of QES potentials that correspond to rationally extended many-body
truncated Calogero-Sutherland model. Our procedure is based upon the potential
group approach with an underlying so(2, 1) structure that utilizes the three
cases guided by it on profitably carrying out a point canonical transformation.
We deal with each case separately by suitably restricting the coupling
parameters.
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