hierarchy problem which is one of the longstanding puzzle in physics. To examine this problem they have introduced two branes located at the boundary of the compactified fifth dimension. The second Randall-Sundrum(RS2) scenario[@rs99-2] is followed from RS1 by remoting one of the brane to infinity. The most remarkable feature of RS2 scenario is that it leads to a massless graviton localized on the 3-brane at the linearized fluctuation level[@garr00; @duff00]. In this paper we will explore the localized RS graviton problem at RS1 and RS2 from the viewpoint of the singular quantum mechanics.

In addition to its good features on hierarchy and localized graviton problem, RS picture supports a non-static cosmological solution[@bine99; @csa99; @cline99] which leads to the conventional Friedmann equation if one introduces the bulk and brane cosmological constants and imposes a particular fine-tuning condition between them. Furthermore, RS scenario is also applied to the cosmological constant hierarchy[@kim01; @alex01] and black hole physics[@cham00; @emp00; @gidd00].

The bulk spacetime of RS scenario is two copies of $AdS_5$ glued in a $Z_2$-symmetric way along a boundary which is interpreted as the 3-brane world-volume. It is explicitly seen by examing the line elements; $$\begin{aligned}
\label{line}
ds^2&=&e^{-2kr_c |\phi|} \eta_{\mu \nu} dx^{\mu} dx^{\nu} + 