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New solutions of Isochronous potentials in terms of exceptional orthogonal polynomials in heterostructures

Point canonical transformation (PCT) has been used to find out new exactly solvable potentials in the position-dependent mass (PDM) framework. We solve $1$-D Schrödinger equation in the PDM framework by considering two different fairly generic position-dependent masses $ (i) M(x)=λg'(x)$ and $(ii) M(x) = c \left( {g'(x)} \right)^ν$, $ν=\frac{2η}{2η+1},$ with $η= 0,1,2\cdots $. In the first case, we find new exactly solvable potentials that depend on an integer parameter $m$, and the corresponding solutions are written in terms of $X_m$-Laguerre polynomials. In the latter case, we obtain a new one parameter $(ν)$ family of isochronous solvable potentials whose bound states are written in terms of $X_m$-Laguerre polynomials. Further, we show that the new potentials are shape invariant by using the supersymmetric approach in the framework of PDM.