Rationally extended many-body truncated Calogero–Sutherland model

Rational extension of many particle systems

“…We would like to find another system related to the TCS model, which is isospectral to the TCS and possibly, its wave functions are written in terms of EOPs. To find the rational extension of the TCS model, we start by adding a new interaction term, [25]…”

“…apart from an overall constant term. Now, l = k + b and α are free parameters and we can chose the parameter α = l such that U ( √ N ρ) = ρ 2 is independent of k. Calogero has shown that the many particle system (25) with U ( √ N ρ) = ρ 2 can be solved exactly for all possible values of k. However, unlike this case, V − (ρ) represents a QES many particle system as we explain below.…”

“…Rational extensions have also been carried out for non-Hermitian systems [6,19,[29][30][31][32]. Even though most of the rational extensions are for the one dimensional and/or one particle exactly solvable systems, the research in this field has also been extended to many particle systems [24,25,27]. We have done several works on rational extensions for many particle systems.…”

“…In one of the works, the well known Calogero-Wolfes type 3-body problem on a line was extended rationally to show that exactly solvable wave functions are written in terms of X m Laguerre and X m Jacobi EOPs [26]. However, this article is based on two of our earlier works on rational extension of many particle systems [24,25], which were central to the talk presented during the AAMP meeting. In the first work [25], we discuss the rational extension of the truncated Calogero-Sutherland model using a PCT approach.…”

“…However, this article is based on two of our earlier works on rational extension of many particle systems [24,25], which were central to the talk presented during the AAMP meeting. In the first work [25], we discuss the rational extension of the truncated Calogero-Sutherland model using a PCT approach. We indicate how to obtain rationally extended solutions, which are isospectral to the original system in terms of X m Laguerre EOPs.…”