The radial supersymmetry of the (d+1)-dimensional relativistic rotating oscillators

We study the supersymmetry of the radial problems of the models of quantum relativistic rotating oscillators in arbitrary dimensions, defined as Klein-Gordon fields in backgrounds with deformed anti-de Sitter metrics. It is pointed out that the shape invariance of the supersymmetric partner radial potentials leads to simple operators forms of the Rodrigues formulas for the normalized radial wave functions.