On first-order scaling intertwining in quantum mechanics

Details On first-order scaling intertwining in quantum mechanics On first-order scaling intertwining in quantum mechanics

2001-02-19

arxiv.org/abs/quant-ph/0102091v1

Rev. Mex. Fis. 46 S2 (Nov. 2000) 153-156

Physics

Quantum Physics

7 pages in LaTex, 1 figure

Scientific paper

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

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