---
abstract: 'The graviton localized on the $3$-brane is examined in Randall-Sundrum brane-world scenario from the viewpoint of one-dimensional singular quantum mechanics. For the Randall-Sundrum single brane scenario the one-parameter family of the fixed-energy amplitude is explicitly computed where the free parameter $\xi$ parametrizes the various boundary conditions at the brane. The general criterion for the localized graviton to be massless is derived when $\xi$ is arbitrary but non-zero. When $\xi=0$, the massless graviton is obtained via a coupling constant renormalization. For the two branes picture the fixed-energy amplitude is in general dependent on the two free parameters. The numerical test indicates that there is no massless graviton in this picture. For the positive-tension brane, however, the localized graviton becomes massless when the distance between branes are infinitely large, which is essentially identical to the single brane picture. For the negative-tension brane there is no massless graviton regardless of the distance between branes and choice of boundary conditions.'
address: 'Department of Physics, Kyungnam University, Masan, 631-701, Korea.'
author:
- 'D. K. Park and Hungsoo Kim'
title: 'Singular Quantum Mechanical Viewpoint of Localized Gravity in Brane-World Scenario'
---

Introduction
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The first Randall-Sundrum(RS1) brane-world scenario[@rs99-1] was designed to solve the gauge 