부산대학교 도서관

The von Roos' position dependent mass Schrödinger Equation (PDMSE) is given in terms of an effective potential, which is constructed by the potential under study and additional terms involving the position dependent mass and the ambiguity ordering parameters. At this regard, some of the most important approaches to the ambiguity parameters are those of BenDaniel-Duke, Gora-Williams, Zhu-Kroemer, Li-Kuhn and so on. In this work we show that for the cases of Zhu-Kroemer and BenDaniel-Duke it is possible to express any solvable potential through a couple of quantum superpotentials. For this, we stablish the factorization of the PDMSE Hamiltonian and the use of a point canonical transformation; these allow to identify a first superpotential W(x). Next, the term in the effective potential with ambiguity parameters is expressed through a function Z(x) and later the cases when Z(x) is a quantum superpotential are discussed. This way, the proposed superpotentials determine the solvable potentials in the PDMSE, the energy spectra and mass functions. We give some examples to explain the approach which can be straightforwardly applied to the solution of the PDMSE for other different potential models and mass distributions. [ABSTRACT FROM AUTHOR]