Four-dimensional gravity on a thick domain wall

We consider an especially simple version of a thick domain wall in AdS space and investigate how four-dimensional gravity arises in this context. The model we consider has the advantage, that: the equivalent quantum mechanics problem can be stated in closed form. The potential in this Schrodinger equation suggests that there could be resonances id the spectrum of the continuum modes. We demonstrate that there are no such resonances in the model we consider. (C) 2000 Elsevier Science B.V. All rights reserved.