  We generalize the standard first-order intertwining relationship of
supersymmetric quantum mechanics in order to include simultaneous scaling
transformations in both the original Hamiltonian and the intertwining operator.
It is argued that in this way one can generate potentials with more interesting
spectra than those obtained by means of the standard first-order intertwining
technique and, as an outcome, a simple engineering procedure is presented. The
harmonic oscillator potential is used in order to illustrate the previous
statements. Moreover, a matrix representation of the scaled intertwining
relationship is sketched up allowing for higher-dimensional generalizations in
the case of separable potentials

Quantum Physics