Poisson kernel $$\label{13-2.19}
K_r(z,\overline{z};\zeta,\overline{\zeta})=
\sum_{k,\,l=0}^{\infty}e^{i\frac{\pi}{4}(k+l)}
\overline{U_{k,\,l}(z,\,\z)}U_{k,\,l}(\zeta,\,\overline{\zeta}),$$ we define the momentum operator $P_X=X^\dag$ conjugate relative basis in the space $\H$ to the coordinate operator. The quadratic Hamiltonian of radial oscillator $$\label{13-2.20}
H_r=\frac{1}{4}\left(X^2+(X^*)^2\right),\quad \text{Dom}[H_r]=\H,$$ is a bounded selfadjoint operator in $\H$. ChK-polynomials $U_{k,\,l}(z,\,\z)$ are eigenfunctions of the operator $H_r$ with eigenvalues $$\label{13-2.21}
\nu_{0\,0}=\frac{4}{5},\quad  \nu_{N\,0}=\nu_{0\,N}=\frac{1}{2}\,\, (\text{for}\, N\geq1),
\quad \nu_{m\,n}=\frac{1}{5}\,\, (\text{for}\, n,m\geq1).$$ To determine the ladder operators we introduce an auxiliary operator $I(\alpha,\beta)$( $\alpha,\beta\in \mathbb{C}$) which acts on the basic elements $U_{k,\,l}(z,\,\z)$ as follows $$\label{13-2.22}
I_B(\alpha;\beta)U_{k,\,l}(z,\,\z)=
\left\{\alpha\left(\delta_{k,N}\delta_{l,0}+\delta_{k,0}\delta_{l,N}\right)
\left(1-\delta_{k,0}\delta_{l,0}\right)+\beta\delta_{k,0}\delta_{l,0}\right\}U_{k,\,l}(z,\,\z).$$ Using this operator, we define the ladder operators of radial oscillator by the relations $$\label{13-2.23}
\arpm=\frac{1}{\sqrt{10}}\left(X+iX^\dag\right)-\frac{2}{\sqrt{5}}\,
I_B\left(\frac{1}{4}\,e^{\pm i\frac{\pi}{4}},\frac{1}{2}\,e^{\pm i\frac{\pi}{4}}\right).$$ From ,, it follows that the action of $\arpm$ looks as $$\label{13-2.24}
\arpm U_{k,\,l}(z,\,\z)=\sqrt{\frac{2}{5}}\,U_{k\pm 1,\,l\pm 1}(z,\,\z).$$ In the work [@N47] we have found the following differential operator representation of the operators $\arpm$: $$a_{rad}^{\pm}\,\rule[-10pt]{.2pt}{20pt}_{\,\H^{(N)}}=\sqrt{\frac{2}{5}}\,
\sum_{m=0}^{N}U_{m\pm 1,\,N-m\pm 1}\frac{\mathbf{D}_{m,\,N-m}}{m!(N-m)!}.$$ The (position) operator is given by the relation $$a_{rad}^{-}+a_{rad}^{+}=\sqrt{\frac{2}{5}}\left\{\rule[-5pt]{0pt}{22pt}
(z\z -3)I-\bigoplus_{N=1}^{\infty}\left[\!\sum_{m=0}^N\frac{\alpha_1}{m!(N-m)!}
-\sum_{m=0}^{N-1}\frac{\alpha_2}{m!(N-m)!}\right]\right\},$$ where $$\begin{gathered}
\alpha_1=U_{m-1,\,N-m+1}\mathbf{D}_{m,N-m}\overline{Z}+
U_{m+1,\,N-m-1}\mathbf{D}_{m,N-m}Z; \\
\alpha_2=U_{m,\,N-m}\mathbf{D}_{m,N-m}+
U_{N-m,\,m}\mathbf{D}_{N-m,m},\end{gathered}$$ and $Z$ , $\overline{Z}$ are the operators of multiplication by $z$ and $\z$, respectively. From -, - we obtain the following expression for the Hamiltonian $H_r$ in terms of the ladder operators $$\label{13-2.28}
H_r=\arp\arm +\arm\arp +I_B\left(\ts\frac{1}{8};\ts\frac{1}{2}\right).$$ Note that, unlike the Hamiltonian $H_s$ 