  We solve Wheeler-De Witt (WDW) metric probability wave equation on the
apparent horizon hypersurface of the Schwarzschild de Sitter (SdS) black hole.
To do so we choose radial dependent mass function $M(r)$ for its internal
regions in the presence of a dynamical massless quantum matter scalar field
$\psi(r)$ and calculate canonical supper hamiltonian constraint on $t-$constant
hypersurface near the horizon $r=M(r)$. In this case $M(r)$ become geometrical
degrees of freedom while $\psi(r)$ is matter degrees of freedom of the apparent
horizon. However our solution is obtained versus the quantum harmonic
oscillator which defined against the well known hermit polynomials. In the
latter case we obtain quantized mass of the SdS quantum black hole as
$\sqrt{\Lambda}M(n)=\big(\frac{2n+1}{12\sqrt{2}}\big)^{\frac{1}{3}}$ in which
$\Lambda$ is the cosmological constant and $n=0,1,2,\cdots $ are quantum
numbers of the hermit polynomials. This shows that a quantized SdS in its
ground state has a nonzero value for the mass $M(0)=0.38914/\sqrt{\Lambda}$.
Thus one can infer that the latter result satisfies Penrose hypotheses for
cosmic censorship where a causal singularity may be covered by a horizon
surface.
