model to the RS2 scenario.

Fixed-Energy Amplitude for RS2
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Recently, one of the present authors computed the fixed-energy amplitude for RS2 at Ref.[@park01-3] which will be reviewed in this section briefly. Furthermore we will derive the general condition in the parameter space for the appearance of the localized massless graviton.

The Hamiltonian for RS2 can be read from Eq.(\[grafluc\]) and (\[potential\]) easily; $$\begin{aligned}
\label{rs2hamil1}
\hat{H}_{RS2}&=&\hat{H}_0 - v \delta(z)    \\   \nonumber
\hat{H}_0&=& -\frac{1}{2} \partial_z^2 + 
\frac{g}{(|z| + c)^2}.\end{aligned}$$ Of course, we can obtain the exact RS2 Hamiltonian by letting $g=15/8$, $c = 1/k \equiv R$ and $v = 3k / 2$, where $R$ is the radius of $AdS_5$. In this section, however, we do not require them from the beginning. In other words we will compute the fixed-energy amplitude for arbitrary $g$, $c$, and $v$ when the half-line constraint ($z \geq 0$) is imposed. This will give us the general condition for the localized graviton on the brane to be massless.

The half-line constraint makes $\hat{H}_0$ in Eq.(\[rs2hamil1\]) to be a following simple form; $$\label{rs2hamil2}
\hat{H}_0 = -\frac{1}{2} \partial_x^2 + \frac{g}{x^2}$$ where $x = z + c$. Thus our half-line constraint $z \geq 0$ is changed into $x \geq c$. 