On first-order scaling intertwining in quantum mechanics

We generalize the standard first-order intertwining relationship of supersy mmetric quantum mechanics in order to include simultaneous scaling transfor mations in both the original Hamiltonian and the intertwining operator. It is argued that in this way one can generate potentials with more interestin g spectra than those obtained by means of the standard first-order intertwi ning technique and, as an outcome, a simple engineering procedure is presen ted. The harmonic oscillator potential is used in order to illustrate the p revious statements, Moreover, a matrix representation of the scaled intertw ining relationship is sketched up allowing for higher-dimensional generaliz ations in the case of separable potentials.