ar X iv : g r - qc / 9 61 00 18 v 1 1 1 O ct 1 99 6 Application of the double Darboux method to the quantum Taub continuum
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چکیده
Application of the double Darboux method to the quantum Taub continuum Abstract The strictly isospectral double Darboux method is applied to the quantum Taub model in order to generate a one-parameter family of strictly isospectral potentials for this case. The family we build is based on a scattering Wheeler-DeWitt solution first discussed by Ryan and collaborators that we slightly modified according to a suggestion due to Dunster. The isospectral Taub potentials possess different (attenuated) scattering states with respect to the original Taub potential. Quantum cosmology and its supersymmetric extension [1] are an interesting " laboratory " for techniques of current use in nonrelativistic quantum mechanics. One such technique is the strictly isospectral double Darboux method, which is intimately connected to Witten's supersymmetric quantum mechanics [2]. We have already applied the double Darboux method to closed, radiation-filled Friedmann-Robertson-Walker (FRW) quantum universes, obtaining a one-parameter family of strictly isospectral FRW quantum potentials and the corresponding wavefunctions [4]. The quantum Taub model is a separable quantum problem [3] and therefore is well suited for the double Darboux procedure. It is our purpose in this paper to develop the method for the Taub case. We start by briefly recalling the Darboux technique of deleting followed by reinstating an energy level of a one-dimensional (1D) potential V (x) by which one can generate a one-parameter family of isospectral potentials V iso (x; λ), where λ is a real, labeling parameter of each member potential in the set. As a matter of fact, Khare and Sukhatme 1
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تاریخ انتشار 1996