us the compromise of the massless graviton with a small cosmological constant[@park01-3].

Toy Model 2: Free Particle in a Box with $\delta$-function Potentials
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In this section as a toy model of RS1 we will examine Green’s function for the free particle system in a $1d$ box($0 \leq x \leq L$) with $\delta$-function potentials at both end points.

The Hamiltonian for this system is $$\label{toy2hamil1}
\hat{H}_{\delta}^{Box} = \hat{H}_0^{Box} - v_1 \delta(x) + v_2 \delta(x - L)$$ where $$\label{toy2hamil2}
\hat{H}_0^{Box} = - \frac{1}{2} \partial_x^2
\hspace{2.0cm}
(0 \leq x \leq L).$$ The main problem in this toy model is of course to derive a fixed-energy amplitude $\hat{G}_0^{Box}$ for $\hat{H}_0^{Box}$. Once $\hat{G}_0^{Box}$ is obtained, the fixed-energy amplitude $\hat{G}_{\delta}^{Box}$ for the total Hamiltonian $\hat{H}_{\delta}^{Box}$ is straightforwardly obtained by performing the Schulman procedure twice; $$\label{toy2schul1}
\hat{G}_{\delta}^{Box}[a, b; E] =
\hat{{\cal G}}_0^{Box}[a, b; E] - 
\frac{\hat{{\cal G}}_0^{Box}[a, L; E] \hat{{\cal G}}_0^{Box}[L, b; E]}
     {\frac{1}{v_2} + \hat{{\cal G}}_0^{Box}[L, L^-; E]}$$ where $$\label{toy2schul2}
\hat{{\cal G}}_0^{Box}[a, b; E] = \hat{G}_0^{Box}[a, b; E]
+ \frac{\hat{G}_0^{Box}[a, 0; E] \hat{G}_0^{Box}[0, b; E]}
       {\frac{1}{v_1} - \hat{G}_0^{Box}[0^+, 0; E]}.$$

The fixed-energy amplitude $\hat{G}_0^{Box}$ for $\hat{H}_0^{Box}$ is also obtained directly from that for free particle on half-line, [*i.e.*]{} $\hat{G}_F^{\xi_1}[a,b; E]$ in Eq.(\[toy1gen1\]). Of course, the 